Qualitative behavior of dissipative wave equations on bounded domains
- Jeffrey Rauch
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The qualitative behavior of solutions of the mixed problem utt = Δu-a(x)ut in IR x Ω, u=0 on IR x ∂Ω, is studied in the case when a>0 and Ω⊂IRn is bounded. Roughly speaking, if a≧amin>0, then solutions decay at least as fast as exp t(ɛ −1/2amin), with the possible exception of a finite dimensional set of smooth solutions whose existence is associated with a phenomenon of overdamping. If amax is sufficiently small, depending on Ω, then no overdamping occurs.
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- Qualitative behavior of dissipative wave equations on bounded domains
Archive for Rational Mechanics and Analysis
Volume 62, Issue 1 , pp 77-85
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- Jeffrey Rauch (1)
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- 1. Department of Mathematics, University of Michigan, Ann Arbor, Michigan