Stability of solutions to nonlinear wave equations with switching time-delay

TL;DR

This paper investigates the well-posedness and asymptotic stability of nonlinear wave equations with switching delay damping, demonstrating stability under certain conditions and providing concrete examples and models.

Contribution

It introduces new stability results for nonlinear wave equations with intermittently switching delay damping and positive-negative damping, expanding understanding of their long-term behavior.

Findings

Asymptotic stability achieved under specific feedback conditions

Concrete examples illustrating the stability results

Stability results for models with alternate positive-negative damping

Abstract

In this paper we study well-posedness and asymptotic stability for a class of nonlinear second-order evolution equations with intermittent delay damping. More precisely, a delay feedback and an undelayed one act alternately in time. We show that, under suitable conditions on the feedback operators, asymptotic stability results are available. Concrete examples included in our setting are illustrated. We give also stability results for an abstract model with alternate positive-negative damping, without delay.