A variational approach to strongly damped wave equations

TL;DR

This paper introduces a Hilbert space method using a new perturbation lemma for sesquilinear forms to establish well-posedness and optimal analyticity angles for strongly damped wave equations.

Contribution

It presents a novel perturbation lemma for sesquilinear forms and extends existing results on strongly damped wave equations using a Hilbert space approach.

Findings

Proves well-posedness of strongly damped wave equations.

Extends known results to broader classes of equations.

Achieves optimal analyticity angles.

Abstract

We discuss a Hilbert space method that allows to prove analytical well-posedness of a class of linear strongly damped wave equations. The main technical tool is a perturbation lemma for sesquilinear forms, which seems to be new. In most common linear cases we can furthermore apply a recent result due to Crouzeix--Haase, thus extending several known results and obtaining optimal analyticity angle.