Asymptotic expansion of solutions to the wave equation with space-dependent damping

Motohiro Sobajima, Yuta Wakasugi

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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 methods with suitable supersolutions of the corresponding parabolic problem.

Original languageEnglish
Pages (from-to)241-279
Number of pages39
JournalAsymptotic Analysis
Volume134
Issue number1-2
DOIs
Publication statusPublished - 2023

Keywords

  • Wave equation
  • asymptotic expansion
  • space-dependent damping

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