In this paper, we study a memory-type porous-elastic system coupled with a neutral delay on the elasticity equation. We construct some appropriate functionals together with modified energy functional and stabilize the...
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In this paper, we study a memory-type porous-elastic system coupled with a neutral delay on the elasticity equation. We construct some appropriate functionals together with modified energy functional and stabilize the system exponentially depending on the wave speed, the weight of the delay, and the relaxation function.
In this article, we investigate a porous-elastic system with dissipation due to only microtemperatures. It is well-known that such a system with a single damping term lacks exponential stability unless another damping...
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In this article, we investigate a porous-elastic system with dissipation due to only microtemperatures. It is well-known that such a system with a single damping term lacks exponential stability unless another damping mechanism is added. In this article, however, we prove that the unique dissipation due to the microtemperatures is strong enough to exponentially stabilize the system if and only if the wave speeds of the system are equal. In the case of lack of exponential stability, we show that the solution decays polynomially. Moreover, we show that this rate of decay is optimal. Our result is new and improves previous results in the literature.
This work deals with the solution and asymptotic analysis for a porous-elastic system with internal damping of the fractional derivative type. We consider an augmented model. The energy function is presented and estab...
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This work deals with the solution and asymptotic analysis for a porous-elastic system with internal damping of the fractional derivative type. We consider an augmented model. The energy function is presented and establishes the dissipativity property of the system. We use the semigroup theory. The existence and uniqueness of the solution are obtained by applying the well-known Lumer-Phillips Theorem. We present two results for the asymptotic behavior: Strong stability of the C0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_0$$\end{document}-semigroup associated with the system using Arendt-Batty and Lyubich-Vu's general criterion and polynomial stability applying Borichev and Tomilov's Theorem.
In this paper, we consider a one-dimensional porous-elastic system with distributed delay term acting on the porous equation. Under suitable assumptions on the weight of distributed delay, we establish the well-posedn...
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In this paper, we consider a one-dimensional porous-elastic system with distributed delay term acting on the porous equation. Under suitable assumptions on the weight of distributed delay, we establish the well-posedness of the system by using semigroup theory and we show that the dissipation given by this complementary control stabilizes exponentially the system for the case of equal speeds of wave propagation.
In this paper, we consider a one-dimensional porous-elastic system with past history and nonlinear damping term. We established the well-posedness using the semigroup theory and we showed that the dissipation given by...
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In this paper, we are considering the one-dimensional porous-elastic system with nonlinear localized damping acting in a arbitrary small region of the interval under consideration. Assuming appropriate assumptions on ...
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In this paper, we are considering the one-dimensional porous-elastic system with nonlinear localized damping acting in a arbitrary small region of the interval under consideration. Assuming appropriate assumptions on the nonlinear terms, we establish the energy decay of the corresponding system. To do this, we used the observability inequality obtained for the conservative system combined with a unique continuation property recently introduced in Ma et al. (Attractors for locally damped Bresse systems and a unique continuation property, 2021. ) and the reduction principle (see Daloutli et al. in Discrete Contin Dyn Syst 2(1):67-94, 2009) where the problem of decay rates with nonlinear damping is reduced to an appropriate stabilizability inequality for the linear equation. This study generalizes and improves previous literature outcomes.
Feng and Apalara (2019) [16] investigated the one-dimensional porous-elastic system with finite memory under the assumptions of equal-speed wave propagations and positive definite energy associated with the solution, ...
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Feng and Apalara (2019) [16] investigated the one-dimensional porous-elastic system with finite memory under the assumptions of equal-speed wave propagations and positive definite energy associated with the solution, and established an optimal explicit energy decay rate. In this paper, we consider the case of non-equal wave speeds and positive semidefinite energy, which are more realistic from the physics point of view. By using the second-order energy, we prove some new decay results that generalize and improve many earlier results in the literature. (C) 2019 Elsevier Inc. All rights reserved.
In this paper, we investigate a one-dimensional porouselasticsystem of memory-type coupled with thermal effects, knowing that the heat flux used was introduced by Green and Naghdi. We establish a general decay resul...
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In this paper, we investigate a one-dimensional porouselasticsystem of memory-type coupled with thermal effects, knowing that the heat flux used was introduced by Green and Naghdi. We establish a general decay result irrespective of any condition among the coefficients of the system.
In this paper, we consider a truncated version for 1D porous-elasticity equations and established exponential decay results by incorporating damping mechanisms of time delay types acting partially on the system. Our a...
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In this work, we establish exponential and polynomial decay results for a one-dimensional porous-elastic system with microtemperatures depending on the system's parameters. Our results are new and improve some pre...
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In this work, we establish exponential and polynomial decay results for a one-dimensional porous-elastic system with microtemperatures depending on the system's parameters. Our results are new and improve some previous literature results where additional damping terms were required to establish the exponential decay result. We also present some numerical tests to illustrate our theoretical results.
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