Abstract wave equations with acoustic boundary conditions

Abstract

We define an abstract setting to treat wave equations equipped with time-dependent acoustic boundary conditions on bounded domains of ${\mathbf{R}}^n$. We prove a well-posedness result and develop a spectral theory which also allows to prove a conjecture proposed in (Gal-Goldstein-Goldstein, J. Evol. Equations 3 (2004), 623-636). Concrete problems are also discussed.

21 pages. A few minor bugs appearing in the journal version have been fixed

References in corpus (1)

• Semigroups For Initial-Boundary Value Problems

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