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We study a nonlinear Cauchy problem modeling the motion of an extensible beam | y t | r y tt + γ Δ 2 y tt + Δ 2 y - a + b | | ∇ y | | 2 + c (∇ y , ∇ y t) Δ y + Δ 2 y t + d (x) h (y t) + f (y) = 0 , in a bounded domain of R N , with clamped boundary conditions in either cases: when r = γ = 0 or else when r and γ are positive. We prove, in both cases, the existence of solutions and the exponential decay of energy. [ABSTRACT FROM AUTHOR]

We are concerned with the isentropic compressible Navier–Stokes system in the two-dimensional torus, with rough data and vacuum; the initial velocity belongs to the Sobolev space H 1 and the initial density is only bounded and nonnegative. Arbitrary regions of vacuum are admissible, and no compatibility condition is required. Under these assumptions and for large enough bulk viscosity, global solutions have been constructed in Danchin and Mucha (Commun Pure Appl Math 76:3437–3492, 2023). The main goal of the paper is to establish that these solutions converge exponentially fast to a constant state, and to specify the convergence rate in terms of the viscosity coefficients. We prove similar exponential decay results for the solutions to the inhomogeneous incompressible Navier–Stokes equations, thereby extending to the torus the recent paper (Danchin et al. in Ann Anal Non Lin IHP, 2023) where bounded domains are considered. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonlinear damped beam equation with logarithmic source and memory term. By using Galerkin method, logarithmic Sobolev inequality, and some compactness arguments, the global existence of weak solutions is obtained. Furthermore, we show the decay estimate of related energy under the smallness assumption on the initial data. [ABSTRACT FROM AUTHOR]

In this paper, an initial boundary value problem of the 2D incompressible Bénard system is concerned. The global existence of a unique strong solution is established by the energy method and a key logarithmic interpolation inequality. In particular, the exponential decay rates for the gradients of velocity and temperature field are obtained. [ABSTRACT FROM AUTHOR]

In this study, we investigate the Lord–Shulman porous elastic system with dissipation caused by the microtemperature effects. Here, the thermal conduction has a single‐phase‐lag that acts as a relaxation time and the energy associated with the solution is not required to be positive definite ξμ∗=μ02$$ \left(\xi {\mu}^{\ast }={\mu}_0^2\right) $$. We introduce a stability number χ$$ \chi $$ and prove using the multiplier technique that the exponential decay of the system is valid if χ=0$$ \chi =0 $$. Otherwise, we show that the system decays polynomially. [ABSTRACT FROM AUTHOR]

We study the wellposedness and the stabilization of solutions of a semilinear wave equation with delay and locally distributed dissipation. The novelty of this paper is that we deal with the semilinear wave equation subject to delay and locally distributed damping without smallness conditions in the initial data or in the delay term. In order to address this, the argumentation requires the use of Strichartz estimates and some microlocal analysis results such as propagation of microlocal defect measures and the Gárard's linearizability property. To obtain the observability estimate in the critical case we prove a Unique Continuation Property for the semilinear wave equation and apply it to our problem. Once we establish essential observability properties for the solutions, it is not difficult to prove that the solutions decay exponentially to 0. [ABSTRACT FROM AUTHOR]

A nonlinear Kirchhoff-type equation with distributed delay and variableexponents is studied. Under suitable hypothesis the blow-up of solutions is proved, and by using an integral inequality due to Komornik the general decay result is obtained in the case b = 0. [ABSTRACT FROM AUTHOR]

In this work, we consider a one-dimensional laminated Timoshenko beam system with thermoelasticity of type III and distributed delay. Our concern is to investigate the exponential stability of the vibrations in the system without structural damping. By exploiting the perturbed energy method with appropriate assumptions on the delay feedback and speeds of wave propagation, we establish that the unique dissipation through the thermal effect is sufficient for exponential decay of the solution even in the presence of distributed delay. [ABSTRACT FROM AUTHOR]

This work deals with a von Kármán system with internal damping. For the solution's existence, we use nonlinear semigroup theory tools. We construct an evolution system by nonlinear Lipschitz perturbation of a semigroup of contractions. We apply the energy method for the asymptotic behavior, which uses suitable multipliers to construct a Lyapunov functional that leads to exponential decay. [ABSTRACT FROM AUTHOR]

In this work, a type III thermo‐porous elastic system is considered. First, we use the semigroup theory to demonstrate that the system is well‐posed. Second, we show that the system is exponentially stable under a natural constraint on its parameters. Finally, we provide various numerical examples to illustrate numerically our theoretical findings. [ABSTRACT FROM AUTHOR]

The survival probability of a quantum system with a finite ground energy is known to decay subexponentially at large times. Here we show that, under the same assumption, the average value of any quantum observable, whenever well-defined, cannot converge exponentially to an extremal value of the spectrum of the observable. Large-time deviations from the exponential decay are therefore a general feature of quantum systems. As a simple application of these results, we show that, when considering an open quantum system whose dynamics is generated by a Hamiltonian with a finite ground energy, a large-time exponential decay of populations is forbidden, whereas coherences may still decay exponentially. [ABSTRACT FROM AUTHOR]

We consider a beam equation in the presence of a leading degenerate operator which is not in divergence form. We impose clamped conditions where the degeneracy occurs and dissipative conditions at the other endpoint. We provide some conditions for the uniform exponential decay of solutions for the associated problem. [ABSTRACT FROM AUTHOR]

This study aims to visualize the motion of an underdamped torsional oscillator using an optical lever. This involves employing an optical setup to magnify and measure the angular displacement of the torsional oscillator as it undergoes oscillations and damps over time. By analysing a video recording of an image of a filament formed by a concave mirror attached to the damped torsional oscillator, we observed an exponential decay in the time-averaged amplitude. [ABSTRACT FROM AUTHOR]

"Inhibition of return" (IOR) was originally described in the field of spatial attention, but it has also been observed in random number generation tasks. Subjects showed a tendency of "repetition avoidance," which can be considered as equivalent to IOR in another cognitive domain. As temporal factors have been suspected to play an important role in random number generation, we aimed to examine how such factors might influence regularities such as repetition avoidance in random number generation tasks. Participants were instructed to verbally generate a sequence of numbers at a certain pace, that is, with either 0.5, 1.5, 3 or 4 s between each response. Each number in the sequence should have the same probability of appearance and should be independent from the others. However, it was observed that the human‐generated sequences differed drastically from computer‐simulated pseudo‐random sequences. The distribution of the repetition gap, which indicates how many different numbers are reported between two identical numbers in the generated sequences, showed a "three‐phase" characteristic: a phase of avoidance of the same number, an oscillatory component for coming back to the same number, and finally an exponential decay of number selection frequencies. This three‐phase characteristic was independent of the time interval between responses. These observations indicate an item‐based process in random number generation, making a time‐based control in this task rather unlikely as has been hypothetically assumed. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the convergence of the fractional relativistic Schrodinger operator (- Δ + m 2) s as s → 1 -. Intuitively, this operator converges to (- Δ + m 2) but the proof of this result is not so simple and it is based on a careful analysis of the involved modified Bessel function K ν . The convergence of the operator makes natural the following question: do the solutions of the problem (- Δ + m 2) s w = f (w) in R N converge, in a suitable sense, to a solution u of the problem (- Δ + m 2) v = f (v) in R N as s → 1 - ? We will show that the answer is affirmative under reasonable hypotheses. The proof of the convergence of solutions is obtained by combining an immersion result for Bessel potential spaces with the uniform convergence on compact sets. To the best of our knowledge, the analogous result for the fractional Laplacian operator (- Δ) s has not been established yet. [ABSTRACT FROM AUTHOR]

In this paper, we provide necessary and sufficient conditions for obtaining the stabilization properties for the one-dimensional Lord–Shulman thermoelastic theory with porosity subject to microtemperature but without temperature where the microtemperature conduction equations are governed by Cattaneo–Maxwell's law. Based on recent results due to Bazarra et al., we introduce a stability number χ 0 involving all coefficients of the system, and we prove that the exponential decay of the corresponding semigroup holds if and only if χ 0 = 0. Otherwise, we show that the system loses exponential stability and its solution decays polynomially with a rate equal to 1 / t . [ABSTRACT FROM AUTHOR]

We study an initial boundary value problem of 2D nonhomogeneous magneto-micropolar equations with density-dependent viscosity in smooth bounded domains. When the initial density can contain vacuum states, we prove that there is a unique global strong solution for the system under the assumption that initial velocity is suitably small. In particular, the initial data can be arbitrarily large except the gradient of velocity. Finally, we obtain the exponential decay rates of strong solutions by using the energy method. [ABSTRACT FROM AUTHOR]

We prove estimates at infinity of convolutions fn★$f^{n\star }$ and densities of the corresponding compound Poisson measures for a class of radial decreasing densities on Rd$\mathbb {R}^d$, d≥1$d \ge 1$, which are not convolution equivalent. Existing methods and tools are limited to the situation in which the convolution f2★(x)$f^{2\star }(x)$ is comparable to initial density f(x)$f(x)$ at infinity. We propose a new approach, which allows one to break this barrier. We focus on densities, which are products of exponential functions and smaller order terms—they are common in applications. In the case when the smaller order term is polynomial, estimates are given in terms of the generalized Bessel function. Our results can be seen as the first attempt to understand the intricate asymptotic properties of the compound Poisson and more general infinitely divisible measures constructed for such densities. [ABSTRACT FROM AUTHOR]

In this paper, we study the stabilization and the partial exact controllability of an inhomogeneous multidimensional thermoelastic diffusion problem by a memory function introduced on a part of the boundary of the material. By using the Nakao difference inequality, we prove that the energy of the system decays to zero exponentially at a rate determined explicitly by the physical parameters. Then by the Hilbert uniqueness method combined with Russell's principle "controllability via stabilizability," we prove that after certain threshold time moment, the considered system is partially controllable under a smallness restriction on the coupling parameters stress-temperature and stress-diffusion. The boundary control function is determined explicitly. [ABSTRACT FROM AUTHOR]

It is known that many physical systems undergoing (nuclear, atomic, etc.) decay do not obey the standard decreasing exponential formula which corresponds to the solution of a first-order, linear ODE having constant coefficients. We propose and solve a new functional equation mathematical model whose solutions are consistent with current experimental data. The basis of our functional representation is centred on the critical role played by the concept of the decay half-life. [ABSTRACT FROM AUTHOR]

In this paper, we consider, from both analytical and numerical viewpoints, a thermoelastic problem. The so-called MGT model, with two different relaxation parameters, is used for both the displacements and the thermal displacement, leading to a linear coupled system made by two third-order in time partial differential equations. Then, using the theory of linear semi-groups the existence and uniqueness to this problem is proved. If we restrict ourselves to the one-dimensional case, the exponential decay of the energy is obtained assuming some conditions on the constitutive parameters. Then, using the classical finite element method and the implicit Euler scheme, we introduce a fully discrete approximation of a variational formulation of the thermomechanical problem. A main a priori error estimates result is shown, from which we conclude the linear convergence under suitable additional regularity conditions. Finally, we present some one-dimensional numerical simulations to demonstrate the convergence of the fully discrete approximation, the behavior of the discrete energy decay and the dependence on a coupling parameter. [ABSTRACT FROM AUTHOR]

Objectives: The aim of this study was to analyze the systolic part of the left ventricular (LV) volume curve obtained by gated myocardial perfusion imaging with the formula used in exponential decay and to investigate the clinical value of the results. Methods: One hundred fifty eight patients were retrospectively enrolled in the study. The study group was divided into three groups as normal, ischemia, and infarct. The systolic portion of the LV volume curve was also analyzed using the exponential decay formula. The scintigraphic parameter obtained using this formula is called the ejection constant (Ec). Results: The Ec results were 1.8±0.8, 2.7±0.9, 3.5±1 in infarct, ischemia, and normal groups, respectively, and the difference in Ec results between the groups was statistically significant (p≤0.001). Conclusion: It appears that Ec may play a clinical role as a scintigraphic parameter in the evaluation of systolic functions of the left ventricle. [ABSTRACT FROM AUTHOR]

This paper aims to analyze the energy decay of the thermoelastic porous system. The dual‐phase lag theory is used to model heat transfer. We consider two perspectives: the classical approach and the second spectrum approach. For the classical approach, the well‐posedness is obtained via the semigroup theory and the system is exponentially stable under equal wave speed conditions. On the opposite, we show a polynomial decay. On the other hand, the well‐posedness of the truncated system is obtained via the Faedo Galerkin method, and the system is exponentially stable without any assumptions on the physical parameters. [ABSTRACT FROM AUTHOR]

Variable-cross-section beams have better mass and strength distribution compared with constant cross-section beams, which can optimize the harvesting power of piezoelectric vibration energy harvesters, which are widely used in self-supplied and low-power electronic devices, providing more convenience and innovation for the development of micromechanical intelligence and portable mobile devices. This paper proposes a piezoelectric energy harvester with a tristable-exponential-decay cross section, which optimizes the strain distribution of the cantilever beam through exponential decay changes to improve the harvesting efficiency of the harvester in low-frequency environments. First, the nonlinear magnetic force is obtained based on the magnetic dipole, and the dynamic model is established by using the Euler–Bernoulli beam theory and Lagrangian equation. The influence of the structural parameters of the harvester on the system dynamics and output characteristics is analyzed in the two dimensions of time and frequency, and the influence of the exponential decay coefficient on the system dynamic response and output power is deeply studied. The research shows that the exponential decay section can reduce the first natural frequency of the cantilever beam; by changing the amplitude, frequency, d and dg of the excitation acceleration, the switching of the monostable, tristable and bistable states of the system can be realized. With a decrease in the exponential decay coefficient, under a low-frequency excitation of 0–7 Hz, the output power of the cantilever beam per unit volume is significantly improved, and under a 4 Hz low-frequency excitation, the acquisition output power per unit volume of the cantilever beam is increased by 7 times, thus realizing low-frequency, high-efficiency energy harvesting. [ABSTRACT FROM AUTHOR]

In this paper we consider the existence and asymptotic behavior of solutions of the following nonlinear Kirchhoff type problem... If the initial energy is appropriately small, we derive the global existence theorem and its exponential decay. [ABSTRACT FROM AUTHOR]

In this work, we are concerned with the well-posedness of solutions as well as the asymptotic behavior of the energy related to the semilinear coupled heat-wave equations, posed on a bounded domain of R n. Inspired by the works (Cavalcanti and Oquendo SIAM J Control Optim. 42:1310-24, 2003) and (Nicaise and Pignotti SIAM J Control Optim. 5(45):1561-85, 2006), we consider dampings in the wave equation and the heat equation, and both dampings have a delay in time. The damping acting on the heat equation is localized and not strategically distributed. In these conditions, we prove that the solutions of this system are exponentially stable. [ABSTRACT FROM AUTHOR]

In this paper, we study the following chemotaxis system with a signal-dependent motility and logistic source: { u t = Δ (γ (v) u) + μ u (1 − u α) , x ∈ Ω , t > 0 , 0 = Δ v − v + u r , x ∈ Ω , t > 0 , u (x , 0) = u 0 (x) , x ∈ Ω under homogeneous Neumann boundary conditions in a smooth bounded domain Ω ⊂ R 2 , where the motility function γ (v) satisfies γ (v) ∈ C 3 ([ 0 , ∞)) with γ (v) > 0 , and | γ ′ (v) | 2 γ (v) is bounded for all v > 0 . The purpose of this paper is to prove that the model possesses globally bounded solutions. In addition, we show that all solutions (u , v) of the model will exponentially converge to the unique constant steady state (1 , 1) as t → + ∞ when μ ≥ K 4 1 + r with K = max 0 < v ≤ ∞ | γ ′ (v) | 2 γ (v) . [ABSTRACT FROM AUTHOR]

In this paper, we investigate a coupled system modeled by fluid and thermoelastic plate, while the heat effects are modeled by the Cattaneo's law giving rise to a "second sound" effect. We proved that the coupled system admits a unique global mild solution. Furthermore, we construct the second-order energy to control the term ‖ ∇ θ ‖ L 2 (Γ 0) so as to establish the exponential decay of the solutions. [ABSTRACT FROM AUTHOR]

Over the years, the stabilization Timoshenko systems with dissipative features have piqued the interest of researchers. The study of Timoshenko systems under various damping effects has resulted in a significant number of studies. When nonphysical assumptions of equal wave velocities are used in stabilization, the expected exponential decay of the energy solution is attained in all recent research. In this study, we analyze a one-dimensional thermooelastic Timoshenko type system in the setting of the second frequency spectrum, where the assumption of equal wave speed is not required for exponential decay to occur. In fact, According to Elishakoff's studies [Elishakoff, Advances in Mathematical Modeling and Experimental Methods for Materials and Structures: The Jacob Aboudi Volume, Dordrecht, The Netherlands: Springer, pp. 249–254, 2009.], we consider the so-called truncated version of the Timoshenko system, and we added a thermoelastic damping according to Green Naghdi law of heat conduction. We first use Faedo–Galerkin approximation to verify the system's global well-posedness. Using a Lyapunov functional we establish an exponential stability without assuming the condition of equal wave speed. A numerical scheme is introduced and analyzed. Finally, assuming extra regularity on the solution, we get some a priori error estimates and we present some numerical results which demonstrate the exponential behavior of the solution. This result significantly improves the previous results in the literature in which equal wave velocities are used to obtain exponential stability. [ABSTRACT FROM AUTHOR]

In this work we study the well-posedness and the asymptotic stability of a linear thermoelastic Timoshenko system free of second spectrum, where the heat conduction is given by Cattaneo's law. We give a detailed proof of the well-posedness, using the semigroup theory. Then, we prove that the system is exponentially stable irrespective of the coefficients. We also illustrate our theoretical results by performing some numerical tests. [ABSTRACT FROM AUTHOR]

In this present study, we pay attention to a class of nonlinear neutral type systems (NNSs) with periodic coefficients and construct some assumptions guaranteeing the exponential stability (ES) of the trivial solutions of the system considered. To get specific conditions guaranteeing the ES, we use a modified Lyapunov functional. In conclusion, we get some estimates for the exponential decay of the solutions at infinity with the constructed sufficient conditions. We give two examples to demonstrate the applicability of the results obtained with the constructed assumptions. [ABSTRACT FROM AUTHOR]

In this article, we deal with a logarithmic wave equation with distributed delay. Firstly, we establish the well-posedness by utilizing the semigroup theory. Later, we obtain the global existence of solutions by using the well-depth method. Moreover, under appropriate assumptions on the weight of the distributed delay and that of strong damping, we get the exponential decay results. [ABSTRACT FROM AUTHOR]

We are interested in the well‐posedness and exponential decay of Moore–Gibson–Thompson equation with memory τ∂tttu+α∂ttu+ht(0)Au+bA∂tu−∫0∞ht′(s)Au(t−s)ds=0.$$ \tau {\partial}_{tt t}u&amp;#x0002B;\alpha {\partial}_{tt}u&amp;#x0002B;{h}_t(0)\mathcal{A}u&amp;#x0002B;b\mathcal{A}{\partial}_tu-{\int}_0&amp;#x0005E;{\infty }{h}_t&amp;#x0005E;{\prime }(s)\mathcal{A}u\left(t-s\right)\mathrm{d}s&amp;#x0003D;0. $$Here, the main feature is that the memory kernel ht(·)$$ {h}_t\left(\cdotp \right) $$ depends on time. By using the linear semigroup theory, we prove that the above system is global well‐posedness. In addition, the exponential decay of the related energy is shown to occur, provided that the memory kernel is controlled by a negative exponential. [ABSTRACT FROM AUTHOR]

We consider the stochastic nonlocal Cahn–Hilliard–Navier–Stokes system with shear-dependent viscosity on a bounded domain M ⊂ R d , d = 2, 3, driven by a multiplicative noise of Lévy and Gaussian types. The velocity u is governed by a Navier–Stokes system with a shear-dependent viscosity controlled by a power p>2. This system is nonlinearly coupled through the Korteweg force with a convective nonlocal Cahn–Hilliard equation for the order parameter φ. The existence of a global weak martingale solution is proved. In the 2D case, we prove the pathwise uniqueness of the weak solution, when 11 / 5 < p < 3. [ABSTRACT FROM AUTHOR]

It is accepted that we cannot obtain the exponential decay of the solutions to the type III thermoelasticity when the dimension of the domain is greater than one. In this short note, we prove that we can show the exponential decay if we consider n2$$ {n}&amp;amp;#x0005E;2 $$ type III dissipative mechanisms whenever the coupling terms satisfy a certain condition. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence, uniqueness, exponential decay, and blow‐up behavior of the viscoelastic beam equation involving the p$$ p $$‐Laplacian operator, strong damping, and a logarithmic source term, given by utt+Δ2u−Δpu+∫0tg(t−s)Δu(s)ds−Δut=ur−2ulnu,inQ=Ω×ℝ+$$ {u}_{tt}+{\Delta}^2u-{\Delta}_pu+{\int}_0^tg\left(t-s\right)\Delta u(s) ds-\Delta {u}_t={\left|u\right|}^{r-2}u\ln \left|u\right|,\kern0.5em \mathrm{in}\kern0.5em Q=\Omega \times {\mathbb{R}}^{+} $$where Ω$$ \Omega $$ is a bounded domain of ℝn$$ {\mathbb{R}}^n $$ and g>0$$ g>0 $$ is a memory kernel. Using the Faedo–Galerkin approximation, we establish the existence and uniqueness result for the global solutions, taking into account that the initial data must belong to an appropriate stability set created from the Nehari manifold. The study of the exponential decay of our problem is based on Nakao's method. Finally, the blow‐up behavior on the instability set is proved. [ABSTRACT FROM AUTHOR]

CARMEN 3 and CARMEN 4 are two missions developed by the CNES to measure flux particle levels in the radiation belts. These two missions consist in embedding the CNES-developed ICARE-NG instrument on both the JASON-3 satellite (LEO: 1336 km, 66°) and the E7C satellite (GEO with EOR posting) for respectively CARMEN 3 and CARMEN 4. During the CARMEN 4 EOR phase (21.06.2019 to 30.10.2019), E7C run through the same L ∗ range ( L ∗ = 3 - 7) as JASON-3 during the same period. As these two satellites are equiped with the same ICARE-NG instrument but are not at the same altitude, it is relevant to compare the electron flux temporal evolution measured on both satellites. Common electron energies measured by ICARE-NG during CARMEN 3 and CARMEN 4 are 1.6 MeV and 1.8 MeV. Studying temporal electron flux evolution for both missions, we notice for both a remarkable exponential decay of the flux level subsequently to a rapid filling of the outer radiation belt due to an important solar activity (geomagnetic storm). This exponential decay is characterised with a timescale τ which depends on the mission, the energy, the L ∗ value, and the concerned exponential decay. These timescales are compared to several previously published estimates. Then, noticing that electron flux temporal evolution have the same dynamics for both missions, we find a projection function from one to the other using classical statistics methods (linear regression, with least squares method). We find that the correlation between CARMEN 3 and CARMEN 4 data depends on the value of Roederer's L ∗ parameter. The r 2 correlation coefficient is higher than 0.6 for L ∗ = 3.5 - 4.8 and smaller otherwise. We notice a global same trend of electron flux temporal evolution from both missions. However, the correlation is limited by irregularities in the electron flux measured by CARMEN 3. The causes of these irregularities are discussed and explained. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a model of poro-thermoelasticity with microtemperatures, where the behavior of the body is influenced by the history of both temperature and microtemperatures. Mathematically, this translates into a system of partial integro-differential equations. Under suitable condition on the tensors appearing in the model, we prove that the resulting system is well posed. In the one-dimensional case, the exponential decay of the energy is proved. [ABSTRACT FROM AUTHOR]

In this work, we analyze the stability of the semigroup associated with a Timoshenko beam model with distributed delay in the rotation angle equation. We show that the type of stability resulting from the semigroup is directly related to some model coefficients, which constitute the velocities of the system's component equations. In the case of stability of the polynomial type, we prove that rate obtained is optimal. We conclude the work performing a numerical study of the solutions and their energies, associated to discrete system. [ABSTRACT FROM AUTHOR]

When it comes to human care service challenges, it is critical to understand the dynamic behavior of the associated contagious diseases because non-Markovian effects play a significant role in their spread. This investigation takes a look into an etiological model directly linked to the complexities of Lassa hemorrhagic fever disease in pregnant women in Africa. This is a bacteriostatic fever and an outbreak illness. The aforesaid ailment in expectant mothers has adverse implications that first popped up in Africa. The etiological model was constructed for the first time utilizing a recently designed fractal-fractional (FF) operator based on the power law, exponential decay, and Mittag-Leffler kernels with fractional order and fractal dimension. We construct three schemes of successive approximations based on FF operators using Lagrange polynomials, and the fundamental reproducing number is determined to be ℛ 0 . The existence and uniqueness of the suggested model's mathematical technique are examined. The endemic and disease-free equilibria are also calculated. Eventually, simulated results of the framework are performed using the suggested numerical approach, and the outcomes in graphical representations quantify the effects of the projected and integrated characteristics and demonstrate that the ailment can be considerably governed or exterminated if the outbreak propagation rate is lessened and the rate of intervention is improved. [ABSTRACT FROM AUTHOR]

We consider the emergence of flocking on the unit-speed model with a time-varying delay. We assume that the delay between two particles is a composition of a delay functional and the spatial distance between the particle's position and the other delayed particle's position. Therefore, the delay depends on the ensemble of all particles and is defined implicitly. For the local existence of the solution, we assume that the delay functional is a C 1 function and its C 1 norm is less than the speed of the particles. Using the unit-speed property and the local solution, we can obtain the global solution. To obtain the asymptotic flocking estimate, we assume that the delay functional is bounded by a linear function of the spatial distance and the coefficients of the linear function are sufficiently small. Under these assumptions on the delay functional, we present a sufficient condition of the initial configuration to obtain the exponential decay for the velocity diameter. We also validate our analytical results with several numerical experiments. [ABSTRACT FROM AUTHOR]

This article is devoted to a study of the question of existence (in time) of weak solutions and the derivation of qualitative properties of such solutions for the nonlinear viscoelastic wave equation with variable exponents and minor damping terms. By using the energy method combined with the Faedo–Galerkin method, the local and global existence of solutions are established. Then, the stability estimate of the solution is obtained by introducing a suitable Lyapunov function. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigating the stability and large time behavior problem on the three‐dimensional Boussinesq equations for magnetohydrodynamic convection near hydrostatic equilibrium by energy method. The stability for the fluids with certain symmetries is built on the spatial domain Ω=R2×T$$ \Omega ={\mathbf{R}}^2\times \mathbf{T} $$ with T=−12,12$$ \mathbf{T}=\left[-\frac{1}{2},\frac{1}{2}\right] $$ being a 1D period box. In addition, the exponential decay of the oscillation parts is established. [ABSTRACT FROM AUTHOR]

In this paper, we consider one-dimensional porous-elastic system in thermoelasticity of type III with delay term in the first equation, Under appropriate assumption on the weight of the delay and by constructing suitable Lyapunov functional, we establish an exponential decay result for the energy of the system in the case of equal speeds of propagation. [ABSTRACT FROM AUTHOR]

We consider a Timoshenko system coupled with heat equations modelled by Cattaneo's law. The coupling is through the transverse displacement. Both ends of the beam are dynamic. One end of the beam is fixed to a base in a translational motion and a tip mass is attached to the other end. We design a feedback control acting at the base. It is shown that this feedback control is a reasonable one and is capable of stabilizing the system. We prove an exponential and a polynomial stability result using the multiplier technique. To this end, we introduce new functionals to form a suitable Lyapunov functional. [ABSTRACT FROM AUTHOR]

In this paper we consider a model of laminated beams combining viscoelastic damping and strong time-delayed damping. The global well-posedness is proved by using the theory of semigroups of linear operators. We prove the lack of exponential stability when the speed wave propagations are not equal. In fact, we show in this situation, that the system goes to zero polynomially with rate t − 1 / 2 . On the other hand, by constructing some suitable multipliers, we establish that the energy decays exponentially provided the equal-speed wave propagations hold. [ABSTRACT FROM AUTHOR]

This paper is mainly concerned with behaviors of solution to the Cauchy problem for a generalized shallow water equation with dispersive term and dissipative term in the Besov space. It is shown that the problem of nonlinear shallow water equation is locally well posed. The H 1 (R) norm of solution to the problem is bounded under certain assumption on the initial value. Several blow-up criteria of solution are presented. The solution has compact support provided that the initial value has compact support. More specifically, the solution exponentially decays at infinity if the initial value exponentially decays at infinity. Our main new contribution is that the effects of coefficients λ and β on solution are illustrated. To the best of our knowledge, the results in Theorems 1.1–1.7 are new. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to investigate the exponential stability of the Timoshenko system in thermoelasticity of second sound with a time-varying delay term in the internal feedback. The well-posedness of the problem is assured by using the variable norm technique of Kato. Furthermore the stability of the system is shown by applying the energy method. [ABSTRACT FROM AUTHOR]

Our main goal in the present work is to prove the well-posedness as well as the exponential stability for a strongly coupled Klein-Gordon system posed on a bounded domain of R 2 with smooth boundary, subject to locally distributed viscoelastic effects driven by nonnegative functions a (x) and b (x) acting on Ω, where a = b = 0 in a region A of Ω. Some difficulties imposed by the presence of integrals terms force us to consider a perturbed problem in order to obtain exponential decay rates. For this purpose, microlocal analysis tools combined with unique continuation property were used. [ABSTRACT FROM AUTHOR]