Operator matrices as generators of cosine operator functions

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.

References in corpus (2)

• Abstract wave equations with acoustic boundary conditions
• Semigroups For Initial-Boundary Value Problems

Cited by in corpus (6)

• On the wave equation with hyperbolic dynamical boundary conditions, interior and boundary damping and supercritical sources
• Damped wave equations with dynamic boundary conditions
• Asymptotics of semigroups generated by operator matrices
• Matrix methods for wave equations
• Higher order operators on networks: hyperbolic and parabolic theory
• Resolvent estimates for the one-dimensional damped wave equation with unbounded damping