Diffusion phenomena for the wave equation with space-dependent damping in an exterior domain

作者：Sobajima Motohiro; Wakasugi Yuta^*

来源：Journal of Differential Equations, 2016, 261(10): 5690-5718.

DOI：10.1016/j.jde.2016.08.006

• Damped wave equation
• Diffusion phenomena
• Friedrichs extensions
• Semigroup estimates
• Weighted energy estimates

In this paper, we consider the asymptotic behavior of solutions to the wave equation with space-dependent damping in an exterior domain. We prove that when the damping is effective, the solution is approximated by that of the corresponding heat equation as time tends to infinity. Our proof is based on semigroup estimates for the corresponding heat equation and weighted energy estimates for the damped wave equation. The optimality of the decay late for solutions is also established.

• 出版日期2016-11-15