Exponential stability of second-order evolution equations with structural damping and dynamic boundary delay feedback

Abstract

We consider a stabilization problem for abstract second-order evolution equations with dynamic boundary feedback laws with a delay and distributed structural damping. We prove an exponential stability result under a suitable condition between the internal damping and the boundary laws. The proof of the main result is based on an identity with multipliers that allows to obtain a uniform decay estimate for a suitable energy functional. Some concrete examples are detailed. Some counterexamples suggest that this condition is optimal.