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This paper focuses on the existence and approximate controllability of second-order non-autonomous impulsive stochastic neutral differential systems in Hilbert spaces. First, by using Schauder's fixed-point theorem, stochastic analysis theory, and evolution operators, a new set of sufficient conditions are formulated, and we prove the existence of mild solutions of second-order non-autonomous impulsive stochastic neutral differential systems. Further, the result is extended to study the approximate controllability results for second-order non-autonomous impulsive stochastic neutral differential systems. Then, a set of sufficient conditions are derived for the approximate controllability of second-order non-autonomous impulsive stochastic neutral differential system by assuming the associated linear system is approximately controllable. The results are obtained with the help of Krasnoselskii's fixed point theorem. Finally, an example is given to illustrate our obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the optimal time decay rates of the higher order spatial derivatives of global solution for the three-dimensional compressible Oldroyd-B model, which was derived independently by Barrett-Lu-Süli [Commun. Math. Sci., 15(5): 1265–1323, 2017] via micro–macro analysis of the compressible Navier–Stokes–Fokker–Planck system. We show that under $ H^3 $ H 3 framework, the third-order spatial derivatives of global small solution of the compressible Oldroyd-B model decay at the rate $ (1+t)^{-\frac 94} $ (1 + t) − 9 4 instead of $ (1+t)^{-\frac 74} $ (1 + t) − 7 4 stated by Wang-Wen [Math. Models Methods Appl. Sci., 30(1): 139–179, 2020]. This decay rate is optimal in the sense that it coincides with that of solutions to heat equation. [ABSTRACT FROM AUTHOR]

This paper is concerned with the initial-boundary value problem for a logarithmic Lamé system with a time delay in a bounded domain. We prove the well-posedness of the system by utilizing the semigroup theory. Then, we prove the existence of global solutions by using the well-depth method. In addition, we establish an exponential stability decay result under appropriate assumptions on the weight of the time delay and that of frictional damping. [ABSTRACT FROM AUTHOR]

In this paper, we consider the inverse coefficients problem of recovering a shear modulus μ and density ρ of a medium from the Neumann-to-Dirichlet map. This inverse problem is motivated by the reconstruction of mechanical properties of tissues in non-destructive testing. We prove Lipschitz stability results for any dimension $ d \geq 2 $ d ≥ 2 , provided that the parameters μ and ρ have upper and lower bounds and belong to a known finite dimensional subspace. The proofs rely on monotonicity relations between the parameters and the Neumann-to-Dirichlet operator, combined with the techniques of localized potentials. [ABSTRACT FROM AUTHOR]

The stability and large-time behavior problem on the magneto-micropolar equations has evoked a considerable interest in recent years. In this paper, we study the stability and exponential decay near magnetic hydrostatic equilibrium to the two-dimensional magneto-micropolar equations with partial dissipation in the domain $ \Omega =\mathbb {T}\times \mathbb {R} $ Ω = T × R . In particular, we takes advantage of the geometry of the domain $ \mathbb {T}\times \mathbb {R} $ T × R to divide u into zeroth mode and the nonzero modes, and obey a strong version of the Poincaré's inequality, which plays a crucial role in controlling the nonlinearity. Moreover, we find that the oscillation part of the solution decays exponentially to zero. Finally, our result mathematically verifies that the stabilization effect of a background magnetic field on magneto-micropolar fluids. [ABSTRACT FROM AUTHOR]

We study some zero-flux attraction-repulsion chemotaxis models, with nonlinear production rates for the chemorepellent and the chemoattractant, whose formulation can be schematized as (⋄) $$\begin{equation} \begin{cases} u_t= \Delta u - \chi \nabla \cdot (u \nabla v)+\xi \nabla \cdot (u \nabla w) & {\rm in}\ \Omega \times (0,T_{\max}),\\ \tau v_t=\Delta v-\varphi(t,v)+f(u) & {\rm in}\ \Omega \times (0,T_{\max}),\\ \tau w= \Delta w - \psi(t,w) + g(u) & {\rm in}\ \Omega \times (0,T_{\max}). \end{cases} \end{equation}$$ { u t = Δ u − χ ∇ ⋅ (u ∇ v) + ξ ∇ ⋅ (u ∇ w) in Ω × (0 , T max) , τ v t = Δ v − φ (t , v) + f (u) in Ω × (0 , T max) , τ w = Δ w − ψ (t , w) + g (u) in Ω × (0 , T max). In this problem, Ω is a bounded and smooth domain of $ \mathbb R^n $ R n , for $ n\geq 2 $ n ≥ 2 , $ \chi,\xi \gt 0 $ χ , ξ > 0 , $ f(u) $ f (u) , $ g(u) $ g (u) reasonably regular functions generalizing, respectively, the prototypes $ f(u)=\alpha u^k $ f (u) = α u k and $ g(u)= \gamma u^l $ g (u) = γ u l , for some $ k,l,\alpha,\gamma \gt 0 $ k , l , α , γ > 0 and all $ u\geq 0 $ u ≥ 0. Moreover, $ \varphi (t,v) $ φ (t , v) and $ \psi (t,w) $ ψ (t , w) have specific expressions, $ \tau \in \{0,1\} $ τ ∈ { 0 , 1 } and $ \Theta :=\chi \alpha -\xi \gamma $ Θ := χ α − ξ γ. Once for any sufficiently smooth $ u(x,0)=u_0(x)\geq 0 $ u (x , 0) = u 0 (x) ≥ 0 , $ \tau v(x,0)=\tau v_0(x)\geq 0 $ τ v (x , 0) = τ v 0 (x) ≥ 0 and $ \tau w(x,0)=\tau w_0(x)\geq 0, $ τ w (x , 0) = τ w 0 (x) ≥ 0 , the local well-posedness of problem ( $ \Diamond $ ◊) is ensured, and we establish for the classical solution $ (u,v,w) $ (u , v , w) defined in $ \Omega \times (0,T_{\max }) $ Ω × (0 , T max) that the life span is indeed $ T_{\max }=\infty $ T max = ∞ and u, v and w are uniformly bounded in $ \Omega \times (0,\infty) $ Ω × (0 , ∞) in the following cases: For $ \varphi (t,v)=\beta v $ φ (t , v) = β v , $ \beta \gt 0 $ β > 0 , $ \psi (t,w)=\delta w $ ψ (t , w) = δ w , $ \delta \gt 0 $ δ > 0 and $ \tau =0 $ τ = 0 , provided (I.1) k 0 , $ \psi (t,w)=\delta w $ ψ (t , w) = δ w , $ \delta \gt 0 $ δ > 0 and $ \tau =1 $ τ = 1 , whenever (II.1) $ l,k\in \left (0,\frac {1}{n}\right ] $ l , k ∈ (0 , 1 n ] ; (II.2) $ l\in \left (\frac {1}{n},\frac {1}{n}+\frac {2}{n^2+4}\right) $ l ∈ (1 n , 1 n + 2 n 2 + 4) and $ k\in \left (0,\frac {1}{n}\right ] $ k ∈ (0 , 1 n ] , or $ k\in \left (\frac {1}{n},\frac {1}{n}+\frac {2}{n^2+4}\right) $ k ∈ (1 n , 1 n + 2 n 2 + 4) and $ l\in \left (0,\frac {1}{n}\right ] $ l ∈ (0 , 1 n ] ; (II.3) $ l,k\in \left (\frac {1}{n},\frac {1}{n}+\frac {2}{n^2+4}\right) $ l , k ∈ (1 n , 1 n + 2 n 2 + 4) . For $ \varphi (t,v)=\frac {1}{|\Omega |}\int _\Omega f(u) $ φ (t , v) = 1 | Ω | ∫ Ω f (u) and $ \psi (t,w)=\frac {1}{|\Omega |}\int _\Omega g(u) $ ψ (t , w) = 1 | Ω | ∫ Ω g (u) and $ \tau =0 $ τ = 0 , under the assumptions k

Pattern dynamics in reaction-diffusion modeling glycolysis are investigated. This paper includes linear stability analysis to deduce the threshold condition for Turing pattern formation and weakly nonlinear analysis to describe the time evolution of the pattern amplitude close to the instability threshold. We will assume that the emerging patterns do not have any spatial structure. We derive a criterion to find the region of parameters for which super/sub-critical Turing instability is possible. Furthermore, we focus on the Turing-Hopf (TH) bifurcation and obtain the reduction of the model to the TH normal forms in order to understand and classify the spatiotemporal dynamics of the model for values of parameters close to the degenerate Turing-Hopf bifurcation point. Our theoretical results are confirmed by numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Cauchy problem of the 3D incompressible Keller–Segel–Navier–Stokes equations with partial diffusion, namely we remove the diffusion $ \Delta \rho $ Δ ρ. Using the damping effect of the growth term $ -\rho ^{3} $ − ρ 3 and the geometry of axisymmetric flow without swirl, we prove the global existence of weak solutions for the system. [ABSTRACT FROM AUTHOR]

In this paper, we study the following nonlinear Schrödinger–Newton system \[ \begin{cases} \Delta u- V(x)u + \Psi u=0, & x\in\mathbb{R}^3, \\ \displaystyle \Delta \Psi+\frac{1}{2} u^2=0, & x\in\mathbb{R}^3, \end{cases} \] { Δ u − V (x) u + Ψ u = 0 , x ∈ R 3 , Δ Ψ + 1 2 u 2 = 0 , x ∈ R 3 , which is a nonlinear system obtained by coupling the linear Schrödinger equation of quantum mechanics with the gravitation law of Newtonian mechanics. Assuming that $ V(y) $ V (y) is radial and satisfies some algebraic decay at the infinity, we construct infinitely many non-radial positive solutions which have polygonal symmetry with respect to $ y_{1} $ y 1 and $ y_{2} $ y 2 and are even in $ y_{2} $ y 2 for the system above by the Lyapunov-Schmidt reduction method. Moreover, we have overcame some new difficulties caused by the non-local term. [ABSTRACT FROM AUTHOR]

In the present paper, we mainly focus on an iterative erythropoiesis model with a nonlinear harvesting term involving a time-varying delay. Under certain conditions and by the Schauder fixed point theorem, we show that the existence of positive periodic solutions can be guaranteed and based on the Banach fixed point theorem, we establish the existence as well as the continuous dependence on parameters theorems of the unique solution. Moreover, two examples are provided to validate the correctness of our outcomes. Our theoretical findings extend and improve several related ones in the existing literature. [ABSTRACT FROM AUTHOR]

The presence of exchange-type source is an important feature of the radiation diffusion model coupled with material heat transfer. In this paper, we prove the existence of continuous weak solutions with compact support for the Cauchy problem of two classes of degenerate diffusion systems with exchange-type sources. One class is weakly coupled and another is special strongly coupled. For special strongly coupled degenerate systems, we further prove that the support of radiation is concurrent with that of material temperature, and the supports are extending as time goes on, which can be derived as a consequence of the exchange mechanism. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of a mathematical model of atherosclerosis in one-dimensional geometry with a free boundary. The motion of the boundary is attributable to the concentration of cells in the intima and their interaction in the subendothelial space in addition to their influx through the boundary. A mathematical model that describes the main inflammatory processes in atherosclerosis is proposed, then, by considering some simplifications, a reduced model is obtained. Using a change of variables, the reduced model is converted to a fixed boundary model with space- and time-dependent coefficients and nonlinear terms. We study the existence of solution for the fixed boundary model starting with a model with linear terms then by applying the fixed point theorem. The wave solution is as well investigated along with numerical simulations. Then, we return to the reduced model, prove the existence of solution and present numerical results. Finally, we generalize the results to the complete model initially proposed. [ABSTRACT FROM AUTHOR]

In this paper, we provide an analytical study of the transmission eigenvalue problem with two conductivity parameters. We will assume that the underlying physical model is given by the scattering of a plane wave for an isotropic scatterer. In previous studies, this eigenvalue problem was analyzed with one conductive boundary parameter whereas we will consider the case of two parameters. We prove the existence and discreteness of the transmission eigenvalues as well as study the dependence on the physical parameters. We are able to prove monotonicity of the first transmission eigenvalue with respect to the parameters and consider the limiting procedure as the second boundary parameter vanishes. Lastly, we provide extensive numerical experiments to validate the theoretical work. [ABSTRACT FROM AUTHOR]

A reaction-diffusion-ODE system of stoichiometric producer-grazer type is considered in this paper. Since the system has nonsmooth nonlinearity, it is shown that the system has new dynamics different from the smooth case. We construct various types of discontinuous steady states and investigate their asymptotic behavior. In addition, the steady-state bifurcation near a constant solution is studied by treating the diffusion coefficient as a bifurcation parameter and the existence of Hopf bifurcation is derived. Our results cover the case where the number of positive equilibria of the kinetic system (i.e. without diffusion) changes from one to three in the spatial interval. Finally, some numerical simulations are given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

To explore the impacts of pulse vaccination on the dynamical behaviors of virus, the current paper investigates the persistence and global attractivity of a diffusive viral infection model incorporated with impulsive CTL immune response while the stronger logistic growth mechanism. Based on the comparison principle and the proper upper and lower solutions, we first discuss the existence of the infection-free steady state, and define the crucial CTL-activated viral infection reproduction number $ R_0 $ R 0 . Then, the fundamental extinction and uniform persistence behaviors of virus are distinguished by various cases of the threshold parameter $ R_0 $ R 0 . Finally, the existence and global attractivity of the positive steady state are still established by employing Brouwer's fixed point theorem and auxiliary functional. Our results indicate that high vaccination rates will stimulate the CTL response more effectively, and thus eventually can force the virus to eradicate. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the globally proper efficiency of set optimization problems. Firstly, we use the so-called certainly set less order relation to define a new kind of set order relation. Based on the new set order relation, we introduce the notion of the globally proper efficient solution of the set optimization problem. Secondly, we establish Lagrange multiplier rule of the set optimization problem. Finally, we obtain Lagrangian duality theorems and saddle point theorems. We also give some examples to illustrate our results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the long-term behaviour of 3D double time-delayed magnetohydrodynamics (MHD)-Voight equations with non-autonomous forcing term. First, we establish the existence, forward compactness and forward stability of pullback attractors by the forward equi-continuity and forward pullback asymptotic compactness of solutions. We then study the upper semi-convergence of pullback attractors as the time parameter tends to positive infinity. Since the solution of this equation has no high regularity, we use the spectrum decomposition technique to prove the forward pointwise pullback asymptotic compactness of solutions. [ABSTRACT FROM AUTHOR]

In this paper, an initial value problem for a nonlinear time-fractional Schrödinger equation with a singular logarithmic potential term is investigated. The considered problem involves the left/forward Hadamard-Caputo fractional derivative with respect to the time variable. Using the test function method with a judicious choice of the test function, we obtain sufficient criteria for the absence of global weak solutions. [ABSTRACT FROM AUTHOR]