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arXiv · 1008.0288

Operator matrices as generators of cosine operator functions

Delio Mugnolo
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Abstract

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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Delio Mugnolo. 2010-08-02. Operator matrices as generators of cosine operator functions. https://doi.org/10.1007/s00020-004-1357-x

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