Dynamics of Partial Differential Equations

Volume 13 (2016)

Number 1

Dedicated to emeritus associate editor Shiyi Chen

Stability of solutions to nonlinear wave equations with switching time delay

Pages: 31 – 51

DOI: http://dx.doi.org/10.4310/DPDE.2016.v13.n1.a2

Authors

G. Fragnelli (Dipartimento di Matematica, Università di Bari, Italy)

C. Pignotti (Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica, Università di L’Aquila, Italy)

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.

Keywords

wave equation, delay feedback, stabilization

2010 Mathematics Subject Classification

35L05, 93D15

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