Explicit decay rate for a degenerate hyperbolic-parabolic coupled system

This paper studies the stability of a 1-dim system which comprises a wave equation and a degenerate heat equation in two connected bounded intervals. The coupling between these two different components occurs at the interface with certain transmission conditions. We find an explicit polynomial decay...

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Bibliographic Details
Published inESAIM. Control, optimisation and calculus of variations Vol. 26; p. 116
Main Authors Han, Zhong-Jie, Wang, Gengsheng, Wang, Jing
Format Journal Article
LanguageEnglish
Published Les Ulis EDP Sciences 2020
Subjects
Decay rate
Degeneration
Diffusion coefficient
Diffusion rate
Polynomials
Thermodynamics
Wave equations
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Summary:This paper studies the stability of a 1-dim system which comprises a wave equation and a degenerate heat equation in two connected bounded intervals. The coupling between these two different components occurs at the interface with certain transmission conditions. We find an explicit polynomial decay rate for solutions of this system. This rate depends on the degree of the degeneration for the diffusion coefficient near the interface. Besides, the well-posedness of this degenerate coupled system is proved by the semigroup theory.
ISSN:1292-8119
1262-3377
DOI:10.1051/cocv/2020040