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In this paper, we are concerned with the asymptotic behavior of solutions to the Cauchy problem (or initial‐boundary value problem) of one‐dimensional Keller–Segel model. For the Cauchy problem, we prove that the solutions time‐asymptotically converge to the nonlinear diffusion wave whose profile is self‐similar solution to the corresponding parabolic equation, which is derived by Darcy's law. For the initial‐boundary value problem, we consider two cases: Dirichlet boundary condition and null‐Neumann boundary condition on (u,ρ)$$ \left(u,\rho \right) $$. In the case of Dirichlet boundary condition, similar to the Cauchy problem, the asymptotic profile is still the self‐similar solution of the corresponding parabolic equation, which is derived by Darcy's law; thus, we only need to deal with boundary effect. In the case of null‐Neumann boundary condition, the global existence and asymptotic behavior of solutions near constant steady states are established. The proof is based on the elementary energy method and some delicate analysis of the corresponding asymptotic profiles. [ABSTRACT FROM AUTHOR]

In this work, we propose a solution to the problem of identification of sources in the brain from measurements of the electrical potential, recorded on the scalp EEG (electroencephalogram), where boundary problems are used to model the skull, brain region, and scalp, solving the inverse problem from the EEG measurements, the so-called Electroencephalographic Inverse Problem (EIP), which is ill-posed in the Hadamard sense since the problem has numerical instability. We focus on the identification of volumetric dipolar sources of the EEG by constructing and modeling a simplification to reduce the multilayer conductive medium (two layers or regions Ω 1 and Ω 2 ) to a problem of a single layer of a homogeneous medium with a null Neumann condition on the boundary. For this simplification purpose, we consider the Cauchy problem to be solved at each time. We compare the results we obtained solving the multiple layers problem with those obtained by our simplification proposal. In both cases, we solve the direct and inverse problems for two different sources, as synthetic results for dipolar sources resembling epileptic foci, and a similar case with an external stimulus (intense light, skin stimuli, sleep problems, etc). For the inverse problem, we use the Tikhonov regularization method to handle its numerical instability. Additionally, we build an algorithm to solve both models (multiple layers problem and our simplification) in time, showing optimization of the problem when considering 128 divisions in the time interval [ 0 , 1 ] s, solving the inverse problem at each time (interval division) and comparing the recovered source with the initial one in the algorithm. We observed a significant decrease in the computation times when simplifying the numerical calculations, resulting in a decrease up to 50 % in the execution times, between the EIP multilayer model and our simplification proposal, to a single layer homogeneous problem of a homogeneous medium, which translates into a numerical efficiency in this type of problem. [ABSTRACT FROM AUTHOR]

This paper develops a mathematical framework that aims to control the temperature and rotational speed in the activation process of a gas turbine in an optimal way. These controls influence the deformation and the stress in the component due to centripetal loads and transient thermal stress. An optimal control problem is formulated as the minimization of maximal von Mises stress over a given time and over the whole component. To find a solution for this, we need to solve the linear thermoelasticity and the heat equations using the finite element method. The results for the optimal control as functions of the rotation speed and external gas temperature over time are computed by sequential quadratic programming, where gradients are computed using finite differences. The overall outcome reveals a significant reduction of approximately 10%, from $ 830\,\frac {{\rm N}}{{\rm mm}^2} $ 830 N mm 2 to $ 750\,\frac {{\rm N}}{{\rm mm}^2} $ 750 N mm 2 , in von Mises stress by controlling two parameters, along with the temporal separation of physical control phenomena. [ABSTRACT FROM AUTHOR]

This paper is concerned with the asymptotic behavior of the solution to the Euler equations with time-depending damping on quadrant (x, t) ∈ ℝ+ × ℝ+, ∂tv−∂xu=0,∂tu+∂xp(v)=−α(1+t)λu,, with the null-Dirichlet boundary condition or the null-Neumann boundary condition on u. We show that the corresponding initial-boundary value problem admits a unique global smooth solution which tends time- asymptotically to the nonlinear diffusion wave. Compared with the previous work about Euler equations with constant coefficient damping, studied by Nishihara and Yang (1999), and Jiang and Zhu (2009, Discrete Contin Dyn Syst), we obtain a general result when the initial perturbation belongs to the same space. In addition, our main novelty lies in the fact that the cut-off points of the convergence rates are different from our previous result about the Cauchy problem. Our proof is based on the classical energy method and the analyses of the nonlinear diffusion wave. [ABSTRACT FROM AUTHOR]

This study delves into the convective heat transfer phenomena within a square cavity that houses a porous medium, analyzing the effects of Darcy (Da) and Rayleigh (Ra) numbers on the thermal and fluid dynamic behavior within the system. Utilizing a combination of computational fluid dynamics (CFD) and the finite element method (FEM), the research focuses on steady-state, laminar flow conditions in two dimensions. The cavity, which is impermeable at its boundaries, contains a centrally located square region filled with a porous, isotropic material. The thermal environment is controlled with insulated horizontal walls and vertically positioned walls that experience sinusoidal temperature variations. The study examines how variations in the permeability of the porous medium (Da numbers ranging from 10−1 to 10−4) and the buoyancy-driven flow strength (Ra numbers spanning from 102 to 105) influence the velocity fields and heat transfer rates, with results expressed through Nusselt number (Nu) distributions. The findings reveal that higher Ra numbers, particularly at 105, significantly intensify convection within the cavity, thereby boosting local rates of heat transfer, especially in the central vertical section. The research identifies that optimal flow resistance in the porous medium occurs within the Da number range of 10−3 to 10−4. These insights are critical for advancing thermal management techniques, particularly in the natural cooling of electronic devices and improving insulation methods. [ABSTRACT FROM AUTHOR]

Copyright of Revista Mexicana de Ingeniería Biomédica is the property of Sociedad Mexicana de Ingenieria Biomedica, A.C. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Biological models for cardiac regeneration and remodeling, along with the effects of cytokines or chemokines during the therapy with mesenchymal stem cells after a myocardial infarction, are of crucial importance for understanding the complex underlying mechanisms. This paper presents a mathematical model composed of three coupled partial differential equations that describes the dynamics of stem cells, nutrients and chemokines, highlighting the fundamental role of the chemokines during the myocardial tissue regeneration process. The system is solved numerically using mimetic difference operators and the MOLE library for MATLAB. The results show the tissue regeneration process in the necrotic part closest to the cell implantation area. [ABSTRACT FROM AUTHOR]

We investigate the minimum cost of a wide class of combinatorial optimization problems over random bipartite geometric graphs in R d where the edge cost between two points is given by a pth power of their Euclidean distance. This includes e.g. the travelling salesperson problem and the bounded degree minimum spanning tree. We establish in particular almost sure convergence, as n grows, of a suitable renormalization of the random minimum cost, if the points are uniformly distributed and d ≥ 3 , 1 ≤ p < d . Previous results were limited to the range p < d / 2 . Our proofs are based on subadditivity methods and build upon new bounds for random instances of the Euclidean bipartite matching problem, obtained through its optimal transport relaxation and functional analytic techniques. [ABSTRACT FROM AUTHOR]

Copyright of Revista Mexicana de Ingeniería Biomédica is the property of Sociedad Mexicana de Ingenieria Biomedica, A.C. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

An SEIR epidemic model with infinite delay and the Neumann boundary condition is investigated, as well as the corresponding free boundary problem, in which the free boundary exactly describes the spreading frontier of the disease. For the problem in a fixed domain with null Neumann boundary condition, the transmission dynamics of the disease is determined by the basic reproduction number R0. More specifically, whether the disease will die out or not depends on R0<1 or R0>1; while for the free boundary problem, we show that under certain conditions the disease will die out even R0>1. Our results indicate that besides the basic reproduction number, the initial size of the infected domain and the diffusivity of the disease in a new region also produce a non-negligible influence to the disease transmission, and it seems more reasonable and acceptable. [ABSTRACT FROM AUTHOR]

Examples are provided of locally integrable vector fields in the plane such that, when restricted to a cuspidate set, require an action concentrated at the cusp to be balanced, no matter what the order of the cusp. Examples are also given of vector fields of the same sort that, in spite of their cusp singularity, are balanced by everywhere null Neumann data at the boundary. All these examples are given explicit thermomechanical interpretations. Collectively, they are meant to support the view that a more general continuum-mechanical theory of contact interactions is needed to complement the standard theory, namely, a theory allowing both for point- or line-concentrated body/environment interactions and for internal interactions concentrated on body parts of zero volume measure. [ABSTRACT FROM AUTHOR]

This paper is concerned with the following chemotaxis-growth system u t = Δ u − ∇ ⋅ u ∇ v + μ (u − u α) , x ∈ Ω , t > 0 , v t = Δ v − v + w , x ∈ Ω , t > 0 , w t = Δ w − w + u , x ∈ Ω , t > 0 , in a smooth bounded domain Ω ⊂ R n (n ⩾ 2) with nonnegative initial data and null Neumann boundary condition, where μ > 0 , α > 1. It is stated that if α > n 4 + 1 2 , the solution is globally bounded. Moreover, if μ > 0 is sufficiently large, the solution (u , v , w) emanating from nonnegative initial data u 0 , v 0 , w 0 with u 0 ⁄ ≡ 0 is globally bounded and satisfies ‖ u ⋅ , t − 1 ‖ L ∞ Ω + ‖ v ⋅ , t − 1 ‖ L ∞ Ω + ‖ w ⋅ , t − 1 ‖ L ∞ Ω → 0 as t → ∞. [ABSTRACT FROM AUTHOR]

We are concerned with the mathematical and numerical modeling of hydrodynamic processes in the Gulf of California. The dynamic is driven by a forcing tide producing an inflow and outflow from the mouth of the Gulf to the northernmost part. When the tidal flow passes through the area of the Islands in the central part of the Gulf, it channels, increasing its speed. On the San Esteban Sill, a hydraulic jump is formed, then internal waves and solitons are released. Based on observational field campaigns, and hydrostatic 3D modeling, it is claimed that this is a cause–effect phenomenon. Hydrostatic models are unable to produce the groups of soliton-like waves. Consequently, we develop a non-hydrostatic version, a 2D vertical-slice model with the inclusion of density effects. Its hydrographic characteristics, such as stratification and bathymetric features, are modeled with appropriate initial and boundary conditions. The numerical solution is by a pressure projection method. The method is tested on benchmark problems and then applied to the Gulf of California. The data of the observational field campaigns are satisfactorily reproduced by the numerical results. [ABSTRACT FROM AUTHOR]

This work aimed to develop numerical models to predict the moisture content and deformation of potato slices during convective drying (40–80 °C, 0.5 m·s−1). Three-dimensional slices were considered in cylindrical, cubic, parallelepiped, and prism geometries. The first classic model coupled the linear constant drying rate period with the analytical solution of Fick's law in spherical coordinates, evaluating the mass diffusion coefficients (4.2–15.5·10−10 m2·s−1), critical drying time (1640–5085 s), and critical moisture content (1.8–2.4 kg·kg−1). The Finite Element Method (FEM) was a more robust model, that combined momentum and mass transfer to three-dimensional solid deformation of polyhedrons by ALE method, evaluating the mass diffusivity (1.4–6.5·10−10 m2·s−1). The FEM model could predict the shrinkage due to water molar flux removal on moving solid boundaries and explain the pseudo-constant drying rate detected in experimental data. The developed models accurately described the drying of food materials with a high shrinkage ratio. [ABSTRACT FROM AUTHOR]

In this paper, we consider a forager–exploiter model with logistic growth and nonlinear resource consumption u t = Δ u − χ 1 ∇ ⋅ (u ∇ w) + η 1 (u − u 2) , x ∈ Ω , t > 0 , v t = Δ v − χ 2 ∇ ⋅ (v ∇ u) + η 2 (v − v 2) , x ∈ Ω , t > 0 , w t = Δ w − u w (1 + u + v) γ − v w (1 + u + v) θ − μ w + r (x , t) , x ∈ Ω , t > 0 in a smooth bounded domain Ω ⊂ R n (n ≥ 1) with nonnegative initial data and null Neumann boundary condition, where χ 1 , χ 2 , η 1 , η 2 , μ > 0 and r is a given nonnegative function. We prove that if γ > 0 and θ > (n − 2) + n + 2 , then the classical solution exists globally and remains bounded. Moreover, the large time behavior is investigated when r satisfies certain conditions. [ABSTRACT FROM AUTHOR]

Film cooling performance was evaluated numerically for three mainstream Reynolds numbers and four blowing ratios (BR). A computational model based on finite volume discretization was used to solve an incompressible and transient flow over a NACA 4412 cascade vane. Several passive scalars were included in the model to evaluate the condition of adiabatic temperature and constant temperature for the surface vane. For the adiabatic temperature condition, the film effectiveness mainly depends on the jet trajectory and recirculation zones. For the constant temperature condition, the net heat flux reduction (NHFR) varies according to the boundary layer separation and reattachment. Consequently, misleading conclusions could be drawn if only one of the two approaches is adopted. For instance, the mainstream Reynolds number Re ∞ = 3615 reached a maximum average effectiveness lower than 0.3 with an average NHFR of 0.25. However, for Re ∞ = 10,845 the maximum average effectiveness was close to 0.45, but with negative average NHFR values. This finding demonstrates the need to explore new indicators like jet trajectory, convective coefficient and skin friction coefficient, as presented in this paper. [ABSTRACT FROM AUTHOR]

The permeability of intact geologic media features prominently in many geo-environmental endeavours. The laboratory estimation of permeability is an important adjunct to the field estimation of bulk permeability values, which involves a great deal of supplementary in situ investigations to correctly interpret field data. Laboratory permeability estimation is also a viable method if core samples are recovered from in situ geological mapping of the region under study. The basic methodologies for permeability estimation rely on either steady-state or transient tests of the geologic material depending on the anticipated permeability value. This paper presents a steady flow test conducted on a partially drilled cavity located on the axis of a cylindrical specimen. Certain compact theoretical relationships are proposed for the estimation of steady flow from a cavity of finite dimensions located along the axis of a cylindrical specimen. The relationships are used to estimate the permeability of a cylinder of Lac du Bonnet granite obtained from the western flank of the Canadian Shield. The results from the cavity flow permeability experiments are compared with other estimates for the permeability of granitic rocks reported in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study the blow-up phenomena of the Dirichlet initial boundary value problem for reaction–diffusion equation with a space–time integral source term. By virtue of Kaplan's technique and some new properties on the system of differential inequalities, the method of constructing blow-up sub-solutions, we establish sufficient conditions to guarantee the solution blows up in finite time and give the upper bounds of life span. Moreover, based on constructing blow-up super-solutions and combining the auxiliary function method with the modified differential inequality techniques, lower bounds of life span are derived. [ABSTRACT FROM AUTHOR]

By comparing model results from tests of steady and oscillatory flows over a submerged bar (of interest for both riverine and marine environments), we highlight similarities and differences between a state-of-the-art Boussinesq model and a recently developed non-hydrostatic, quasi-three-dimensional (3D) model. To make the comparison as clean as possible, the complexities due to breaking-induced turbulence are avoided by suitably tuning the flow strength. Although the main flow features are similarly described by the two models, the non-hydrostatic model predicts the occurrence of extra, small-scale stationary oscillations on top of a submerged obstacle in the case of a steady current. This is attributed to a pattern of alternating upward and downward vertical velocity over the sill top, presumably due to rapidly converging flows as they climb over the submerged obstacle. The non-hydrostatic model overall allows for a more complete representation of flow dynamics in the vertical direction, with respect to the Boussinesq-type solver. This becomes necessary when tackling fundamental and applicative problems characterized by intense vertical flows (e.g., interactions of fluids with structures). [ABSTRACT FROM AUTHOR]

In this paper, we consider a mathematical model of dengue transmission with the symptomatic and asymptomatic infected subclasses in the human population and exposed subclasses in both human and mosquito populations. We ignore the movement of humans because our interest is to study the local dengue propagation throughout small regions. In our model, the dynamics of the mosquito population is described by advection–diffusion partial differential equations and that of the human population is considered as a homogeneous distribution in space. The basic reproduction number, R 0 , is obtained using the next-generation approach. We show that if R 0 < 1 , the disease-free equilibrium is globally asymptotically stable and if R 0 > 1 , a unique endemic equilibrium emerges and it is locally asymptotically stable. In addition, when R 0 > 1 , we investigate the rate of dengue dissemination by determining the minimum speed c ∗ of traveling wave solutions, if they exist. Next, we seek to approximate c ∗ for the proposed model. Finally, we verify the existence of traveling wave solutions by presenting some numerical simulations. [ABSTRACT FROM AUTHOR]

Copyright of Hydrogeology Journal is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Seasonality is the common phenomena in ecological evolution. Firstly, we formulate and explore a simplified West Nile virus model, which describes the transmission of West Nile virus driven by seasonal fluctuations in a spatially variable habitat where the spatial movement of the infectious mosquitoes and infectious birds are described by Laplace diffusion. The range of the infected area is assumed to be a moving interval [0,h(t)] ⊂ ℝ, with its right end point representing the spreading fronts of the disease. We will mainly investigate the impact of spatial heterogeneity of environment and temporal periodicity on the persistence and extinction of West Nile virus. The basic reproduction number R0D in a fixed region and the spatial-temporal risk index R0F (t) for the free boundary problem, which depends on spatial heterogeneity, temporal periodicity and spatial diffusion, are defined by the associated linearized eigenvalue problems. Sufficient conditions for the spreading and vanishing of West Nile virus are presented for the spatial dynamics of the virus. At last, we explore the long time dynamical behavior of the solution to free boundary problem when the spreading occurs. [ABSTRACT FROM AUTHOR]

This paper deals with the qualitative properties of solutions for null Neumann initial boundary value problem to a nonlocal pseudo-parabolic equation in the sense of H 1 (Ω) -norm. We establish sufficient conditions to guarantee that the solution with initial energy exists globally or blows up at finite time under an appropriate range of parameters. Moreover, life span of the blow-up solution, decay rate of the global solution, and growth estimate are derived. [ABSTRACT FROM AUTHOR]

When modelling contamination transport in the subsurface and aquifers, it is crucial to assess the heterogeneities of the porous medium, including the vertical distribution of the aquifer parameter. This issue is generally addressed thanks to geophysical investigations. As an alternative, a method is proposed using estimated hydraulic parameters from a 2D calibrated flow model (solely reliant on piezometric series) as parametrization constraints for a 3D hydrogeological model. The methodology is tested via a synthetic model, ensuring full knowledge and control of its structure. The synthetic aquifer is composed of five lithofacies, distributed according to a sedimentary pattern, and functions in an unconfined regime. The level of heterogeneity for hydraulic conductivity spans 3 orders of magnitude. It provides the piezometric chronicles used to inverse 2D flow parameter fields and the lithological logs used to interpolate the 3D lithological model. Finally, the parameters of each facies (hydraulic conductivity and porosity) are obtained through an optimization loop, which minimizes the difference between the 2D calibrated transmissivity and the transmissivity computed with the estimated 3D facies parameters. The method estimates values close to the known parameters, even with sparse piezometric and lithological data sampling. The maximal discrepancy is 45 % of the known value for the hydraulic conductivity and 6 % for the porosity (mean error 26 % and 3 %, respectively). Although the methodology does not prevent interpolation errors, it succeeds in reconstructing flow and transport dynamics close to the control data. Due to the inherent limitations of the 2D inversion approach, the method only applies to the saturated zone at this point. [ABSTRACT FROM AUTHOR]

Full-waveform inversion (FWI) is a high-resolution numerical technique for seismic waves used to estimate the physical characteristics of a subsurface region. The continuous problem involves solving an inverse problem on an infinite domain, which is impractical from a computational perspective. In limited area models, absorbing boundary conditions (ABCs) are usually imposed to avoid wave reflections. Several relevant ABCs have been proposed, with extensive literature on their effectiveness on the direct wave problem. Here, we investigate and compare the theoretical and computational characteristics of several ABCs in the full inverse problem. After a brief review of the most widely used ABCs, we derive their formulations in their respective adjoint problems. The different ABCs are implemented in a highly optimized domain-specific language (DSL) computational framework, Devito, which is primarily used for seismic modelling problems. We evaluate the effectiveness, computational efficiency, and memory requirements of the ABC methods, considering from simple models to realistic ones. Our findings reveal that, even though the popular perfectly matching layers (PMLs) are effective at avoiding wave reflections at the boundaries, they can be computationally more demanding than less used hybrid ABCs. We show here that a proposed hybrid ABC formulation, with nested Higdon's boundary conditions, is the most cost-effective method among the methods considered here, for being as effective as or more effective than PML and other schemes but also for being computationally more efficient. [ABSTRACT FROM AUTHOR]

These lecture notes address the controllability under state constraints of reaction-diffusion equations arising in socio-biological contexts. We restrict our study to scalar equations with monostable and bistable nonlinearities.The uncontrolled models describing, for instance, population dynamics, concentrations of chemicals, temperatures, etc., intrinsically preserve pointwise bounds of the states that represent a proportion, volume-fraction, or density. This is guaranteed, in the absence of control, by the maximum or comparison principle.We focus on the classical controllability problem, in which one aims to drive the system to a final target, for instance, a steady-state. In this context the state is required to preserve, in the presence of controls, the pointwise bounds of the uncontrolled dynamics.The presence of constraints introduces significant added complexity for the control process. They may force the needed control-time to be large enough or even make some natural targets to be unreachable, due to the presence of barriers that the controlled trajectories might not be able to overcome.We develop and present a general strategy to analyze these problems. We show how the combination of the various intrinsic qualitative properties of the systems' dynamics and, in particular, the use of traveling waves and steady-states' paths, can be employed to build controls driving the system to the desired target.We also show how, depending on the value of the Allee parameter and on the size of the domain in which the process evolves, some natural targets might become unreachable. This is consistent with empirical observations in the context of endangered minoritized languages and species at risk of extinction.Further recent extensions are presented, and open problems are settled. All the discussions are complemented with numerical simulations to illustrate the main methods and results. [ABSTRACT FROM AUTHOR]

We study the homogeneous Dirichlet problem for the degenerate parabolic equation of the Kirchhoff type ut−a(‖∇u‖22)Δu=b(‖u‖22)|u|q(x,t)−2uinQT=Ω×(0,T),where T > 0, Ω⊂ℝn, n ≥ 2, is a smooth bounded domain. The exponent q(x, t) is a measurable function in QT with values in an interval [q−, q+] ⊂ (1, ∞). The coefficients a(·), b(·) are continuous functions defined on ℝ+. It is assumed that a(s) → 0 or a(s) → ∞ as s → 0+; therefore, the equation degenerates or becomes singular as ‖ ∇ u(t)‖2 → 0. We prove the local in time solvability of the problem and derive sufficient conditions of the finite time blow‐up of the nonnegative solutions. The upper and lower estimates on the blow‐up moment are found. [ABSTRACT FROM AUTHOR]

In this article, we will determine the source term of the fractional diffusion equation (FDE). Our contribution to this work is the generalization of the common inverse diffusion equation issues and the inverse diffusion equation problems for fractional diffusion equations with energy source and using Caputo fractional derivatives in time and space. The problem is reformulated in a least-squares framework, which leads to a nonconvex minimization problem, which is solved using a Tikhonov regularization. By considering the direct problem with an implicit finite difference scheme (IFDS), the numerical inversions are performed for the source term in several approximate spaces. The inversion algorithm (IA) uniqueness is obtained. Furthermore, the effect of fractional order and regularization parameter on the inversion algorithm is carried out and shows that the inversion algorithm is effective. The order of fractional derivatives expresses the global property of the direct problem and also shows the badly posed nature of the inverted problem in question. [ABSTRACT FROM AUTHOR]

The study of polymer flooding is of utmost relevance due to the diversity of applications. This paper proposes an innovative mathematical and computational model for polymer flooding that efficiently couples the process in the near-well region and the reservoir. For the mathematical model, in addition to the single-phase flow and transport equations, we postulate closure relationships for the adsorption isotherms, mechanical retention kinetics, and non-Newtonian pseudoplastic behavior. For the computational model, we propose a space-time domain decomposition method based on a predictor-corrector strategy. The resulting system of equations is discretized by the finite element method and linearized by the Newton-Raphson method. Moreover, we apply a consistent flux method to obtain the flow at the boundaries and quantify the injectivity ratio. Then, we validate the accuracy of the proposed method by comparing the discrete solutions with analytical and high-fidelity solutions. We also discuss the loss of injectivity due to the non-Newtonian behavior, mechanical retention, and formation damage at 2D and 3D domains that replicate a five-spot injection pattern. The numerical simulations show that the proposed computational model accurately captures the solutions with low computational costs in several scenarios for polymer injection in porous media. [ABSTRACT FROM AUTHOR]

Water-flooding aided by electromagnetic (EM) heating using microwaves (MW) has a great potential for heavy oil recovery. Earlier, we have shown experimentally and theoretically that EM radioactive energy is absorbed by water and converted into heat near the EM source. The heat is imparted into the oil phase while being transported deep into the porous medium (Paz et al. in Transp Porous Media 119(1):57–75, 2017). The lowering of water is primarily responsible for the improved oil recovery in this process. This paper develops a model describing electromagnetic heating-assisted water flooding (EMA WF) in a thin heavy oil reservoir. The model is solved numerically using a staggered algorithm joining Galerkin Least Square Finite Elements Method (GLS-FEM) and Kurganov–Tadmor Finite Volumes Method (KT-FVM). Numerical results were obtained for different types of oil. For the considered parameter values, the EM heating technique increments the oil production up to 56% after a 24-month injection. This increment is inversely proportional to the oils API gravity. The implementation was validated by comparing computational results with the simplified model's analytical solution obtained using Conservation Laws theory and the Sturm–Liouville theory. Simple convergence analysis was also performed endorsing our numerical approach. Both analytical and numerical approaches were obtained for the two-dimensional geometry with two parallel horizontal wells. The temperature profile obtained through the simplified model's analytical solution is close to the one obtained by simulations (less than 1.9% relative error). [ABSTRACT FROM AUTHOR]

In this paper, we give a probabilistic interpretation for solutions to the Neumann boundary problems for a class of semi-linear parabolic partial differential equations (PDEs for short) with singular non-linear divergence terms. This probabilistic approach leads to the study on a new class of backward stochastic differential equations (BSDEs for short). A connection between this class of BSDEs and semi-linear PDEs is established. [ABSTRACT FROM AUTHOR]

This paper presents a new mesoscopic full field approach for the modeling of microstructural evolutions and mechanical behavior of olivine aggregates. The mechanical framework is based on a reduced crystal plasticity (CP) formulation which is adapted to account for non-dislocation glide strain-accommodating mechanisms in olivine polycrystals. This mechanical description is coupled with a mixed velocity–pressure finite element (FE) formulation through a classical crystal plasticity finite element method (CPFEM) approach. The microstructural evolutions, such as grain boundary migration and dynamic recrystallization, are also computed within a FE framework using an implicit description of the polycrystal through the level-set approach. This numerical framework is used to study the strain localization, at the polycrystal scale, on different types of pre-existing shear zones for thermomechanical conditions relevant to laboratory experiments. We show that both fine-grained and crystallographic textured pre-existing bands favor strain localization at the sample scale. The combination of both processes has a large effect on strain localization, which emphasizes the importance of these two microstructural characteristics (texture and grain size) on the mechanical behavior of the aggregate. Table summarizes the list of the acronyms used in the following. [ABSTRACT FROM AUTHOR]

This paper deals with a quasilinear predator-prey model with indirect prey-taxis u t = ∇ · (D (u) ∇ u) - ∇ · (S (u) ∇ w) + r u g (v) - u h (u) , (x , t) ∈ Ω × (0 , ∞) , w t = d w Δ w - μ w + α v , (x , t) ∈ Ω × (0 , ∞) , v t = d v Δ v + f (v) - u g (v) , (x , t) ∈ Ω × (0 , ∞) , under homogeneous Neumann boundary conditions in a smooth bounded domain Ω ⊂ R n , n ≥ 1 , where d w , d v , α , μ , r > 0 and the functions g , h , f ∈ C 2 ([ 0 , ∞)) . The nonlinear diffusivity D and chemosensitivity S are supposed to satisfy D (s) ≥ a (s + 1) - γ a n d 0 ≤ S (s) ≤ b s (s + 1) β - 1 for all s ≥ 0 , with a , b > 0 and γ , β ∈ R . Suppose that γ + β < 1 + 1 n and γ < 2 n , it is proved that the problem has a unique global classical solution, which is uniformly bounded in time. In addition, we derive the asymptotic behavior of globally bounded solution in this system according to the different predation conditions. [ABSTRACT FROM AUTHOR]

In this work, a new discretization of the source term of the shallow water equations with non-flat bottom geometry is proposed to obtain a well-balanced scheme. A Smoothed Particle Hydrodynamics Arbitrary Lagrangian-Eulerian formulation based on Riemann solvers is presented to solve the SWE. Moving-Least Squares approximations are used to compute high-order reconstructions of the numerical fluxes and, stability is achieved using the a posteriori MOOD paradigm. Several benchmark 1D and 2D numerical problems are considered to test and validate the properties and behavior of the presented schemes. [ABSTRACT FROM AUTHOR]

This paper deals with the blow-up phenomenon of solutions to a reaction–diffusion equation with weighted nonlocal gradient absorption terms in a bounded domain. Based on the method of auxiliary function and the technique of modified differential inequality, we establish appropriate conditions on weight function and nonlinearities to guarantee the solution exists globally or blows up at finite time. Moreover, upper and lower bounds for blow-up time are derived under appropriate measure in higher dimensional spaces. [ABSTRACT FROM AUTHOR]

Abstract This paper deals with the qualitative properties of solutions for null Neumann initial boundary value problem to a nonlocal pseudo-parabolic equation in the sense of H1(Ω) $H^{1}(\varOmega )$-norm. We establish sufficient conditions to guarantee that the solution with initial energy exists globally or blows up at finite time under an appropriate range of parameters. Moreover, life span of the blow-up solution, decay rate of the global solution, and growth estimate are derived.

In recent years, the Asian gall wasp Dryocosmus kuriphilus has invaded chestnut trees and significantly affected the Portuguese chestnut production. Studies in other countries, such as Japan or Italy, have shown that the parasitoid Torymus sinensis can successfully achieve biological control of D. kuriphilus. Mathematical models help us to understand the dynamics of the interaction between the pest D. kuriphilus and its parasitoid T. sinensis and, consequently, they can help to implement measures that enhance crop pest management. In this work, the evolution of the density of D. kuriphilus and T. sinensis across time and space is studied through the numerical solution of models that include parameters based on observations made in Portugal. Simultaneous releases of the parasitoid are simulated at various locations and at different times. The results indicate that, in the case of a small and homogeneous orchard, biological control can be effective, but, in the case of extensive domains, the pest control is much more difficult to achieve. In order for biological control to be efficient, it is necessary to implement, in each chestnut-producing region, a collective strategy based on the annual monitoring of infestation levels. [ABSTRACT FROM AUTHOR]

The Baranyi--Roberts model describes the dynamics of the volumetric densities of two interacting cell populations. We randomize this model by considering that the initial conditions are random variables whose distributions are determined by using sample data and the principle of maximum entropy. Subsequenly, we obtain the Liouville--Gibbs partial differential equation for the probability density function of the two-dimensional solution stochastic process. Because the exact solution of this equation is unaffordable, we use a finite volume scheme to numerically approximate the aforementioned probability density function. From this key information, we design an optimization procedure in order to determine the best growth rates of the Baranyi--Roberts model, so that the expectation of the numerical solution is as close as possible to the sample data. The results evidence good fitting that allows for performing reliable predictions. [ABSTRACT FROM AUTHOR]

This paper deals with a fully parabolic singular chemotaxis-(growth) system with indirect signal production or consumption u t = Δ u - χ ∇ · u v ∇ v + f (u) , (x , t) ∈ Ω × (0 , ∞) , v t = Δ v + h (v , w) , (x , t) ∈ Ω × (0 , ∞) , w t = Δ w - w + u , (x , t) ∈ Ω × (0 , ∞) , under homogeneous Neumann boundary conditions in a smooth convex bounded domain Ω ⊂ R 2 , where χ > 0 . When f (u) = 0 , h (v , w) = - v + w , we prove that the solution (u, v, w) of this model is globally uniformly bounded in time and exponentially converges to the steady state (u 0 ¯ , u 0 ¯ , u 0 ¯) in the norm of L ∞ (Ω) provided that χ < χ 0 with χ 0 > 0 , where u 0 ¯ : = 1 | Ω | ∫ Ω u 0 (x) d x . Moreover, in the case of f (u) = r u - μ u 2 , h (v , w) = - v + w , where r ∈ R , and μ > 0 , we obtain the global existence of solutions for this system. Furthermore, under the conditions of f (u) = r u - μ u 2 , h (v , w) = - v w and μ > 0 , r > 0 , the solution (u, v, w) is also global in time. [ABSTRACT FROM AUTHOR]

In numerous polycrystalline materials, grain size is controlled by second phase particles (SPPs) that hinder the grain boundaries (GBs) by pinning mechanisms. The Smith–Zener pinning (SZP) model describes the physical interaction between SPPs and GBs. Both of them can evolve when applying a heat treatment to the material. As industrial forging processes involve hot deformation steps near the solvus temperature, it is thus of prime importance to characterize the evolution of the SPPs due to their impact on the final microstructure, notably on the grain size. The level set (LS) method is classically used to describe the influence of SPPs on grain growth (GG) by considering the simulated particles as inert and represented by static holes in the used finite element (FE) mesh. A new formalism to model GG mechanism under the influence of the SZP phenomenon, able to take into account evolving particles is proposed. It involves the representation of SPPs by a LS function and a particular numerical treatment around the grain interfaces encountering SPP, making possible the modelling of SPPs evolution without altering the undergoing pinning pressure. Validation and comparison of the new method regarding previous FE-LS formulation in 2D and 3D simulations and an application on GG under the influence of dissolving particles are described. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a reaction–diffusion–advection model with expanding fronts, which models the spatial transmission of West Nile virus (WNv) in a heterogeneous environment. A free boundary problem is formulated and the global existence and uniqueness of the solution is presented. In addition to a classical basic reproduction number, the spatial-temporal basic reproduction number for the model with null Dirichlet boundary condition is introduced and the risk index associated with the virus in spatial setting is defined, and their properties are discussed. Sufficient conditions for the WNv to vanish or spread are given, and the asymptotic behavior of the solution to the free boundary problem when the spreading occurs is established. Our results show that the initial number of infected populations and the expanding capability of the expanding fronts exhibit important impacts on the extinction or persistence of the virus. [ABSTRACT FROM AUTHOR]

This work is concerned with the Neumann initial boundary value problem and Cauchy problem of a parabolic p‐Laplacian equation with nonlocal Fisher–KPP type reaction terms. We establish a uniform boundedness and global existence of solutions to the equation by applying the method of multipliers and modified Moser's iteration technique for some ranges of parameters. The ranges of parameters have similar structure to that of the classical critical Fujita exponent. [ABSTRACT FROM AUTHOR]