English

Operator matrices as generators of cosine operator functions

Analysis of PDEs 2018-12-21 v1

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 Lp(0,1)L^p(0,1) and in L2(Ω)L^2(\Omega) equipped with dynamical and acoustic-like boundary conditions, respectively.

Keywords

Cite

@article{arxiv.1008.0288,
  title  = {Operator matrices as generators of cosine operator functions},
  author = {Delio Mugnolo},
  journal= {arXiv preprint arXiv:1008.0288},
  year   = {2018}
}
R2 v1 2026-06-21T15:55:54.354Z