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Abstract wave equations with acoustic boundary conditions. (English) Zbl 1109.47035
The paper is devoted to the study of wave equations equipped with time-dependent acoustic (or absorbing) boundary conditions in bounded domains in $$\mathbb{R}^n$$. The author discusses the proper setting for the problem, proves a well-posedness result for the abstract initial value problem and deals with some spectral properties of an operator matrix involved. Concrete problems are also discussed.

##### MSC:
 47D06 One-parameter semigroups and linear evolution equations 47H20 Semigroups of nonlinear operators 37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) 35L20 Initial-boundary value problems for second-order hyperbolic equations 35L05 Wave equation 34G10 Linear differential equations in abstract spaces 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs 35P05 General topics in linear spectral theory for PDEs
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