Damped wave equations with dynamic boundary conditions

Abstract

We discuss several classes of linear second order initial-boundary value problems, where damping terms appear in the main wave equation as well as in the dynamic boundary condition. We investigate their well-posedness and describe some qualitative properties of their solutions, including boundedness, stability, or almost periodicity. In particular, we are able to characterize the analyticity of certain $C_0$-semigroups associated to such problems. Applications to several problems on domains and networks are shown.

References in corpus (5)

• Gaussian estimates for a heat equation on a network
• Variational and Semigroup Methods for Waves and Diffusion in Networks
• Semigroups For Initial-Boundary Value Problems
• Operator matrices as generators of cosine operator functions
• Matrix methods for wave equations

Cited by in corpus (3)

• On the the wave equation with hyperbolic dynamical boundary conditions, interior and boundary damping and source
• On the wave equation with hyperbolic dynamical boundary conditions, interior and boundary damping and supercritical sources
• Asymptotics of semigroups generated by operator matrices