Energy decay rate for a nonlinear von Kármán equation with memory

Abstract

This paper is concerned with energy decay rates for a nonlinear von Kármán equation with infinite memory and rotational inertia. We obtain decay rate 1/t only under a monotonicity condition on the memory kernel g, besides basic conditions for the wellposedness of the equation. The advantage of this lies in the fact that without assuming any of the various estimates of the derivative of g or other additional conditions required in the previously related results on von Kármán systems, we obtain an explicit decay rate, which is optimal in some sense.