On the Kirchhoff plates equations with thermal effects and memory boundary conditions

摘要

In this paper we study the existence of weak and strong global solutions and uniform decay of the energy to the Kirchhoff plates equations with thermal effect and memory conditions working at the boundary. We show that the dissipation produced by the memory effect not depend on the present values of 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 decays exponentially. When the relaxation functions decays polynomially, we show that the solution decays polynomially with the same rate.