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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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2011/274843 |
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| _version_ | 1832568465110597632 |
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| author | Moncef Aouadi |
| author_facet | Moncef Aouadi |
| author_sort | Moncef Aouadi |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-ec8711262e614b9183e8ff88c7af8ae0 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-ec8711262e614b9183e8ff88c7af8ae02025-02-03T00:59:08ZengWileyInternational 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 |
| spellingShingle | Moncef Aouadi Exponential Stability in Hyperbolic Thermoelastic Diffusion Problem with Second Sound International Journal of Differential Equations |
| title | 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_short | Exponential Stability in Hyperbolic Thermoelastic Diffusion Problem with Second Sound |
| title_sort | exponential stability in hyperbolic thermoelastic diffusion problem with second sound |
| url | http://dx.doi.org/10.1155/2011/274843 |
| work_keys_str_mv | AT moncefaouadi exponentialstabilityinhyperbolicthermoelasticdiffusionproblemwithsecondsound |