Asymptotic expansion of solutions to the wave equation with space-dependent damping
arXiv:2203.06360 · doi:10.3233/ASY-231834
Abstract
We study the large time behavior of solutions to the wave equation with space-dependent damping in an exterior domain. We show that if the damping is effective, then the solution is asymptotically expanded in terms of solutions of corresponding parabolic equations. The main idea to obtain the asymptotic expansion is the decomposition of the solution of the damped wave equation into the solution of the corresponding parabolic problem and the time derivative of the solution of the damped wave equation with certain inhomogeneous term and initial data. The estimate of the remainder term is an application of weighted energy method with suitable supersolutions of the corresponding parabolic problem.
33 pages
References in corpus (3)
- Remarks on an elliptic problem arising in weighted energy estimates for wave equations with space-dependent damping term in an exterior domain
- Higher order asymptotic expansion of solutions to abstract linear hyperbolic equations
- Supersolutions for parabolic equations with unbounded diffusion and its applications to some classes of parabolic and hyperbolic equations