Exponential Stability in Hyperbolic Thermoelastic Diffusion Problem with Second Sound

Exponential Stability in Hyperbolic Thermoelastic Diffusion Problem with Second Sound

We consider a thermoelastic diffusion problem in one space dimension with second sound. The thermal and diffusion disturbances are modeled by Cattaneo's law for heat and diffusion equations to remove the physical paradox of infinite propagation speed in the classical theory within Fourier'...

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Main Author: Moncef Aouadi
Format: Article
Language:English
Published: Hindawi Limited 2011-01-01
Series:International Journal of Differential Equations
Online Access:http://dx.doi.org/10.1155/2011/274843
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spelling doaj-ec8711262e614b9183e8ff88c7af8ae02020-11-24T20:46:27ZengHindawi LimitedInternational Journal of Differential Equations1687-96431687-96512011-01-01201110.1155/2011/274843274843Exponential Stability in Hyperbolic Thermoelastic Diffusion Problem with Second SoundMoncef Aouadi0Département de Mathématique, Institut Supérieur des Sciences Appliquées et de Technologie de Mateur, Route de Tabarka, Mateur 7030, TunisiaWe consider a thermoelastic diffusion problem in one space dimension with second sound. The thermal and diffusion disturbances are modeled by Cattaneo's law for heat and diffusion equations to remove the physical paradox of infinite propagation speed in the classical theory within Fourier's law. The system of equations in this case is a coupling of three hyperbolic equations. It poses some new analytical and mathematical difficulties. The exponential stability of the slightly damped and totally hyperbolic system is proved. Comparison with classical theory is given.http://dx.doi.org/10.1155/2011/274843
collection DOAJ
language English
format Article
sources DOAJ
author Moncef Aouadi
spellingShingle Moncef Aouadi
Exponential Stability in Hyperbolic Thermoelastic Diffusion Problem with Second Sound
International Journal of Differential Equations
author_facet Moncef Aouadi
author_sort Moncef Aouadi
title Exponential Stability in Hyperbolic Thermoelastic Diffusion Problem with Second Sound
title_short Exponential Stability in Hyperbolic Thermoelastic Diffusion Problem with Second Sound
title_full Exponential Stability in Hyperbolic Thermoelastic Diffusion Problem with Second Sound
title_fullStr Exponential Stability in Hyperbolic Thermoelastic Diffusion Problem with Second Sound
title_full_unstemmed Exponential Stability in Hyperbolic Thermoelastic Diffusion Problem with Second Sound
title_sort exponential stability in hyperbolic thermoelastic diffusion problem with second sound
publisher Hindawi Limited
series International Journal of Differential Equations
issn 1687-9643
1687-9651
publishDate 2011-01-01
description We consider a thermoelastic diffusion problem in one space dimension with second sound. The thermal and diffusion disturbances are modeled by Cattaneo's law for heat and diffusion equations to remove the physical paradox of infinite propagation speed in the classical theory within Fourier's law. The system of equations in this case is a coupling of three hyperbolic equations. It poses some new analytical and mathematical difficulties. The exponential stability of the slightly damped and totally hyperbolic system is proved. Comparison with classical theory is given.
url http://dx.doi.org/10.1155/2011/274843
work_keys_str_mv AT moncefaouadi exponentialstabilityinhyperbolicthermoelasticdiffusionproblemwithsecondsound
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