Abstract
We derive an energy decay estimate for solutions to the initial-boundary value problem of a semilinear wave equation in exterior domains with a nonlinear localized dissipation. Our equation includes an absorbing term like |u| αu, α ≥ 0, and can be regarded as a generalized Klein-Gordon equation at least if α is closed to 0. This observation plays an essential role in our argument.
Original language | English |
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Pages (from-to) | 851-883 |
Number of pages | 33 |
Journal | Journal of the Mathematical Society of Japan |
Volume | 64 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2012 |
Externally published | Yes |
Keywords
- Energy decay
- Localized dissipation
- Nonlinear wave equation
ASJC Scopus subject areas
- Mathematics(all)