Operator matrices as generators of cosine operator functions

Details Operator matrices as generators of cosine operator functions Operator matrices as generators of cosine operator functions

2010-08-02

arxiv.org/abs/1008.0288v1

Integral Equations and Operator Theory 54 (2006), 441-464

Mathematics

Analysis of PDEs

Scientific paper

We introduce an abstract setting that allows to discuss wave equations with time-dependent boundary conditions by means of operator matrices. We show that such problems are well-posed if and only if certain perturbations of the same problems with homogeneous, time-independent boundary conditions are well-posed. As applications we discuss two wave equations in $L^p(0,1)$ and in $L^2(\Omega)$ equipped with dynamical and acoustic-like boundary conditions, respectively.

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