Explicit decay rate for a degenerate hyperbolic-parabolic coupled system.

Buttazzo, G.; Casas, E.; de Teresa, L.; Glowinsk, R.; Leugering, G.; Trélat, E.; Zhang, X.; Han, Zhong-Jie; Wang, Gengsheng; Wang, Jing

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.

HEAT equation; DIFFUSION coefficients; DEGENERATE parabolic equations; DEGENERATE differential equations; SOCIAL degeneration; POLYNOMIALS; WAVE equation

ESAIM: Control, Optimisation & Calculus of Variations, 2020, Vol 26, p1

1292-8119

Academic Journal

10.1051/cocv/2020040