Flexible structure with second sound and past history– existence, uniqueness and exponential stability

Abstract

In this paper, we concerned with a flexible structure system with past history acting only in one equation, where the heat flux is given by Cattaneo's law. Under suitable hypotheses on the relaxation function g, we
prove the wellposed of the system and show that the dissipation given by the history term is strong enough to produce exponential stability without any restriction or relation on the coefficients of the system.