Exponential stability for second order evolutionary problems

Abstract

We study the exponential stability of evolutionary equations. The focus is laid on second order problems and we provide a way to rewrite them as a suitable first order evolutionary equation, for which the stability can be proved by using frequency domain methods. The problem class under consideration is broad enough to cover integro-differential equations, delay-equations and classical evolution equations within a unified framework.

Example 2.1 added, Remark 2.3 (former Remark 2.2) part (c) added, Misprint in Proposition 3.6 (former Proposition 3.5) corrected, References updated