Long-time Behavior for a Nonlinear Plate Equation with Thermal Memory

Abstract

We consider a nonlinear plate equation with thermal memory effects due to non-Fourier heat flux laws. First we prove the existence and uniqueness of global solutions as well as the existence of a global attractor. Then we use a suitable Lojasiewicz--Simon type inequality to show the convergence of global solutions to single steady states as time goes to infinity under the assumption that the nonlinear term \(f\) is real analytic. Moreover, we provide an estimate on the convergence rate.