General boundary stabilization of memory-type thermoelasticity

Messaoudi, Salim A.; Al-Shehri, Aisha

doi:10.1063/1.3496995

Cited by 9 publications

(8 citation statements)

References 32 publications

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“…Similar parabolic-hyperbolic systems to the ones presented in the introduction have been analyzed in [25,26]. Thermoelasticity system in n dimensions with short memory are studied in [27,28] and are commented in last section.…”

Section: Preprintsmentioning

confidence: 98%

Global Non-existence of a Coupled Parabolic-Hyperbolic System of Thermoelastic Type with History

Esquivel-Avila

2023

Preprint

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We consider two abstract systems of parabolic-hyperbolic type that model thermoelastic problems. We study the influence of the physical constants and the initial data on the nonexistence of global solutions that in our framework are produced by the blow-up in finite time of the norm of the solution in the phase space. We employ a differential inequality to find sufficient conditions that produce the blow-up. To that end, we construct a set that is positive invariant for any positive value of the initial energy. As a result we found that the coupling with the parabolic equation stabilizes the system, as well as the damping term in the hyperbolic equation. Moreover, for any pair of positive values $(\xi,\epsilon)$, there exist initial data such that the corresponding solution with initial energy $\xi$ blows-up at a finite time less than $\epsilon$. Our purpose is to improve results previously published in the literature.

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Section: Preprintsmentioning

confidence: 98%

Global Non-existence of a Coupled Parabolic-Hyperbolic System of Thermoelastic Type with History

Esquivel-Avila

2023

Preprint

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“…Some analytical methods (cf. [12][13][14][22][23][24]), such as the generalized variational principle, Laplace transform method, eigenfunction expansion method and energy method, have been put forward to research the properties of analytical solutions for various thermo-elasticity models. However, it is very difficult for us to obtain the analytical solutions of the generalized models with arbitrary initial-boundary conditions.…”

Section: Mathematical Model and Related Studiesmentioning

confidence: 99%

A Two-Level Crank-Nicolson Difference Scheme and Its Richardson Extrapolation Methods for a Magneto-Thermo-Elasticity Model

Dingwen Deng,

Ruyu Zhang

2024

AAMM

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This study is concerned with numerical solutions of a Magneto-Thermo-Elasticity (MTE) model via a combination of energy-conserving finite difference method (FDM) with Richardson extrapolation methods (REMs). Firstly, by introducing two auxiliary functions and using second-order centered FDM and Crank-Nicolson method to approximate spatial and temporal derivatives, respectively, a two-level energy-conserving FDM is established for a MTE model. The priori estimation, solvability, and convergence are derived rigorously by using the discrete energy method. Secondly, to improve computational efficiency, a class of REMs are also designed by constructing the symbolic expansion of numerical solutions. Finally, numerical results confirm the efficiency of the proposed algorithms and the exactness of the theoretical findings.

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“…Different mechanisms have been utilized to stabilize such systems and several decay and stability results have been obtained. In this regard we mention, among many others, the work of Dafermos [2], Messaoudi and Al-Shehri [3], Muñoz Rivera [7], Rivera and Barreto [8], Rivera and Racke [9], Racke and Shibata [11].…”

Section: Introductionmentioning

confidence: 99%

“…where k is the resolvent kernel of −g /g(0). Messaoudi and Al-Shehri [3] considered (1.2) for a wider class of kernels k satisfying…”

Section: Introductionmentioning

confidence: 99%

General stabilization of a thermoelastic systems with a boundary control of a memory type

Semchedine¹,

Benseridi²,

Drabla

2022

Stud. Univ. Babes-Bolyai Math.

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"In this paper we consider an n-dimensional thermoelastic system, in a bounded domain, where the memory-type damping is acting on a part of the boundary and where the resolvent kernel k of ${-g^{\prime }(t)}/{g(0)} $ satisfies\linebreak $k^{\prime \prime }(t)\geq \gamma \left( t\right) (-k^{\prime }(t))^{p}$, $t\geq 0$, $1< p<\frac{3}{2} $. We establish a general decay result, from which the usual exponential and polynomial decay rates are only special cases. This work generalizes and improves earlier results in the literature."

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General boundary stabilization of memory-type thermoelasticity

Cited by 9 publications

References 32 publications

Global Non-existence of a Coupled Parabolic-Hyperbolic System of Thermoelastic Type with History

Global Non-existence of a Coupled Parabolic-Hyperbolic System of Thermoelastic Type with History

A Two-Level Crank-Nicolson Difference Scheme and Its Richardson Extrapolation Methods for a Magneto-Thermo-Elasticity Model

General stabilization of a thermoelastic systems with a boundary control of a memory type

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