Dynamics of Partial Differential Equations
Volume 13 (2016)
Dedicated to emeritus associate editor Shiyi Chen
Stability of solutions to nonlinear wave equations with switching time delay
Pages: 31 – 51
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.
wave equation, delay feedback, stabilization
2010 Mathematics Subject Classification