Exponential stability for second order evolutionary problems

TL;DR

This paper investigates the exponential stability of second order evolutionary equations by transforming them into first order problems and applying frequency domain methods, covering a broad class including integro-differential and delay equations.

Contribution

It introduces a unified approach to analyze exponential stability of second order problems by rewriting them as first order equations and applying frequency domain techniques.

Findings

Provides a method to establish exponential stability for a broad class of second order evolutionary problems.

Unifies the analysis of integro-differential, delay, and classical evolution equations.

Offers a framework that simplifies stability proofs for complex evolutionary equations.

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.