Matrix methods for wave equations

Abstract

In analogy to a characterisation of operator matrices generating $C_0$-semigroups due to R. Nagel (\cite{[Na89]}), we give conditions on its entries in order that a $2\times 2$ operator matrix generates a cosine operator function. We apply this to systems of wave equations, to second order initial-boundary value problems, and to overdamped wave equations.

References in corpus (2)

• Abstract wave equations with acoustic boundary conditions
• Operator matrices as generators of cosine operator functions

Cited by in corpus (6)

• Damped wave equations with dynamic boundary conditions
• Asymptotics of semigroups generated by operator matrices
• Maximal $L^p$-regularity and $H^{\infty }$-calculus for block operator matrices and applications
• Diffusion systems and heat equations on networks
• A variational approach to strongly damped wave equations
• Resolvent estimates for the one-dimensional damped wave equation with unbounded damping