Document Zbl 1020.35042

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Dirichlet boundary stabilization of the wave equation. (English) Zbl 1020.35042

Asymptotic Anal. 30, No. 2, 117-130 (2002).

Summary: We consider the stabilization problem for a wave equation. In the case when the geometric control assumption is not satisfied, we prove that the energy of the system decays with a logarithmic rate for all initial data in the domain of the infinitesimal generator of the evolution equation. The technique used consists in deducing the decay estimate from an observability inequality for the associated undamped problem, via sharp regularity results.

Cited in 1 Review

Cited in 24 Documents

MSC:

35L20	Initial-boundary value problems for second-order hyperbolic equations
93D15	Stabilization of systems by feedback
35B35	Stability in context of PDEs

Keywords:

Dirichlet type boundary feedback; decay estimate; observability inequality

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