Optimal Decay Rate Estimates of a Nonlinear Viscoelastic Kirchhoff Plate

Abstract EN

This paper is concerned with a nonlinear viscoelastic Kirchhoff plate uttt−σΔuttt+Δ2ut−∫0tgt−sΔ2usds=divF∇ut.

By assuming the minimal conditions on the relaxation function g: g′t≤ξtGgt, where G is a convex function, we establish optimal explicit and general energy decay results to the system.

Our result holds for Gt=tp with the range p∈1, 2, which improves earlier decay results with the range p∈1,3/2.

At last, we give some numerical illustrations and related comparisons.