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Diffusion phenomena for the wave equation with space-dependent damping in an exterior domain.
- Source :
-
Journal of Differential Equations . Nov2016, Vol. 261 Issue 10, p5690-5718. 29p. - Publication Year :
- 2016
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 261
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 118235489
- Full Text :
- https://doi.org/10.1016/j.jde.2016.08.006