On a von Kármán plate system with free boundary and boundary conditions of memory type

Abstract

In this paper we study the existence of weak and strong global solutions and uniform decay of the energy to a von Kármán system for Kirchhoff plates equations with thermal effects and memory conditions working at the boundary. We show that the dissipation produced by the memory effect does not depend on the present values of the temperature gradient. That is, we show that the dissipation produced by memory effect is strong enough to produce exponential decay of the solution provided the relaxation functions also decay exponentially. When the relaxation functions decay polynomially, we show that the solution decays polynomially with the same rate.