Asymptotics of semigroups generated by operator matrices

Abstract

We survey some known results about operator semigroup generated by operator matrices with diagonal or coupled domain. These abstract results are applied to the characterization of well-/ill-posedness for a class of evolution equations with dynamic boundary conditions on domains or metric graphs. In particular, our ill-posedness results on the heat equation with general Wentzell-type boundary conditions complement those previously obtained by, among others, Bandle-von Below-Reichel and Vitillaro-Vázquez.

References in corpus (8)

• Abstract wave equations with acoustic boundary conditions
• Heat equation with dynamical boundary conditions of reactive-diffusive type
• A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains
• Damped wave equations with dynamic boundary conditions
• Semigroups For Initial-Boundary Value Problems
• Operator matrices as generators of cosine operator functions
• Matrix methods for wave equations
• Markovian Extensions of Symmetric Second Order Elliptic Differential Operators

Cited by in corpus (4)

• Optimal control of stochastic differential equations with dynamical boundary conditions
• Long-time behavior of stochastically perturbed neuronal networks
• Stochastic reaction-diffusion equations on networks
• Some remarks on the Krein--von Neumann extension of different Laplacians