Volume 26, 2020
Special issue in honor of Enrique Zuazua's 60th birthday
|Number of page(s)||20|
|Published online||17 December 2020|
Explicit decay rate for a degenerate hyperbolic-parabolic coupled system*
School of Mathematics, Tianjin University, P.R. China.
2 Center for Applied Mathematics, Tianjin University, P.R. China.
3 School of Mathematics and Statistics, Beijing Institute of Technology, P.R. China.
** Corresponding author: firstname.lastname@example.org
Accepted: 4 July 2020
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.
Mathematics Subject Classification: 35B40 / 93D20
Key words: Polynomial decay / C0 semigroup / coupled heat-wave equation / degenerate coefficient
© EDP Sciences, SMAI 2020
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