A Note on the Asymptotic Stability of Wave-Type Equations with Switching Time-Delay

Serge Nicaise (1) , Cristina Pignotti (2)

1 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015
2 DISIM - Department of Information Engineering, Computer Science and Mathematics = Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica [L'Aquila]

We consider second-order evolution equations with intermittently delayed/not-delayed damping. We give sufficient conditions for asymptotic and exponential stability, completing our previous results from Nicaise and Pignotti [Adv. Diff. Eq., 17: 879–902, 2012; J. Dyn. Diff. Eq., 26: 781–803, 2014]. Moreover, some concrete models are described.

Mots clés: wave equation; stabilization; switching time delay type feedbacks

Domaines: Equations aux dérivées partielles [math.AP]

Serge Nicaise, Cristina Pignotti. A Note on the Asymptotic Stability of Wave-Type Equations with Switching Time-Delay. Kais Ammari; Stephane Gerbi. Evolution Equations: Long Time Behavior and Control, 1, Cambridge University Press, pp.137-150, 2017, 9781108412308. ⟨10.1017/9781108304023.007⟩. ⟨hal-03142598⟩