Stability of a degenerate thermoelastic equation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917798348849152 |
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| author | Ammari, Kaïs Hassine, Fathi Robbiano, Luc |
| author_facet | Ammari, Kaïs Hassine, Fathi Robbiano, Luc |
| contents | This work is dedicated to the study of a linear model arising in thermoelastic rod of homogeneous material. The system is resulting from a coupling of a heat and a wave equation in the interval $(0,1)$ with Dirichlet boundary conditions at the outer endpoints where the parabolic component is degenerating at the end point $x=0$. Two models are considered the first is with weak degeneracy and the second is with strong degeneracy. We aim to study the well-posedness and asymptotic stability of both systems using techniques from the $C_{0}$-semigroup theory and a use a frequency domain approach based on the well-known result of Prüss in order to prove using some multiplier techniques that the energy of classical solutions decays uniformly as time goes to infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06732 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of a degenerate thermoelastic equation Ammari, Kaïs Hassine, Fathi Robbiano, Luc Analysis of PDEs Dynamical Systems This work is dedicated to the study of a linear model arising in thermoelastic rod of homogeneous material. The system is resulting from a coupling of a heat and a wave equation in the interval $(0,1)$ with Dirichlet boundary conditions at the outer endpoints where the parabolic component is degenerating at the end point $x=0$. Two models are considered the first is with weak degeneracy and the second is with strong degeneracy. We aim to study the well-posedness and asymptotic stability of both systems using techniques from the $C_{0}$-semigroup theory and a use a frequency domain approach based on the well-known result of Prüss in order to prove using some multiplier techniques that the energy of classical solutions decays uniformly as time goes to infinity. |
| title | Stability of a degenerate thermoelastic equation |
| topic | Analysis of PDEs Dynamical Systems |
| url | https://arxiv.org/abs/2410.06732 |