Optimal Dcay Rate Estimates of a Nonlinear Viscoelastic Kirchhoff Plate

This paper is concerned with a nonlinear viscoelastic Kirchhoff plate u(tt)(t) - sigma Delta u(tt)(t) + Delta(2)u(t)- integral(t)(0) g(t - s)Delta(2)u(s)ds = divF(del u(t)). By assuming the minimal conditions on the relaxation function g: g' (t) <= xi (t)G (g(t)), where G is a convex function, we establish optimal explicit and general energy decay results to the system. Our result holds for G(t) = tp with the range p is an element of [1, 2), which improves earlier decay results with the range p is an element of [1, 3/2). At last, we give some numerical illustrations and related comparisons.