Exponential stability and global existence in thermoelasticity with radial symmetry
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In this paper, the authors consider equations of linear and nonlinear thermoelasticity with various boundary conditions and assume radial symmetry of the initial data to prove exponential decay and show the global existence of solutions of the nonlinear problem for small initial data.Abstract:
In this paper we consider equations of linear and nonlinear thermoelasticity with various boundary conditions. We assume radial symmetry of the initial data to prove exponential decay and to show the global existence of solutions of the nonlinear problem for small initial data.read more
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Book
The theory of partial differential equations
TL;DR: In this article, Fourier series and Fourier transforms have been used to describe fundamental theory, evolution equations, and semi-linear hyperbolic equations, as well as a number of others.
Journal ArticleDOI
Initial Boundary Value Problems in Mathematical Physics
TL;DR: Leis as mentioned in this paper gave an account of some recent developments in the theory of partial differential equations for readers thoroughly familiar with functional analysis, dealing with various types of problem for the wave equation, Maxwell's equations, Schrodinger's equation, the plate equation etc.
Book ChapterDOI
Chapter 4 – Thermoelasticity
TL;DR: In this article, an extensive discussion of initial boundary value problems in thermoelasticity is presented, including the comparison to classical thermo-elasticities. But the authors focus on the hyperbolic-parabolic model with Fourier's law of heat conduction and do not discuss the asymptotic behavior of solutions.
Journal ArticleDOI
Global Existence in Nonlinear Hyperbolic Thermoelasticity with Radial Symmetry
TL;DR: In this article, the authors considered a nonlinear system of hyperbolic thermoelasticity in two or three dimensions with DIRICHLET boundary conditions in the case of radial symmetry.
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Optimal Decay Rate for Unidimensional Thermoelastic Problem within the Green-Lindsay Model
Moncef Aouadi,Taoufik Moulahi +1 more
TL;DR: In this paper, the authors considered the generalized thermoelasticity under Green-Lindsay model in one dimension with Dirichlet-Neumann boundary conditions and proved the exponential decay of the associated energy and described the optimal decay rate.
References
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Shock Waves and Reaction-Diffusion Equations
TL;DR: In this paper, the basics of hyperbolic conservation laws and the theory of systems of reaction-diffusion equations, including the generalized Morse theory as developed by Charles Conley, are presented in a way accessible to a wider audience than just mathematicians.
Controlabilite exacte, perturbations et stabilisation de systemes distribues
TL;DR: Controle optimal de systemes. (Systemes couples) as mentioned in this paper : Cas of systemes soumis a des perturbations. Controlabilite exacte and perturbation singulieres.
Book
The theory of partial differential equations
TL;DR: In this article, Fourier series and Fourier transforms have been used to describe fundamental theory, evolution equations, and semi-linear hyperbolic equations, as well as a number of others.
Book
Initial Boundary Value Problems in Mathematical Physics
TL;DR: In this paper, the authors present an introduction both to classical scattering theory and to the time-dependent theory of linear equations in mathematical physics, using Hibert space methods to develop the latter theory in such a way that the asymptotic behaviour of large time can be discussed.