Exponential stabilization of a neutrally delayed wave equation

Abstract

We study of the memory a wave equation with a distributed neutral delay. We prove that, despite the destructive nature of delays in general, solutions may go back to the equilibriun state in an exponential manner as time goes to infinity. Reasonable conditions on the distributed neutral delay are established. This type of problems appear in the study of wave propagation in viscoelatic media and in acoustic wave propagation. It is not well studied so far. 30