STABILITY FOR A VISCOELASTIC PLATE EQUATION WITH p-LAPLACIAN

Abstract

In this paper, we consider a viscoelastic plate equation with p-Laplacian <TEX>$u^{{\prime}{\prime}}+{\Delta}^2u-div({\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)+{\sigma}(t){\int}_{0}^{t}g(t-s){\Delta}u(s)ds-{\Delta}u^{\prime}=0$</TEX>. By introducing suitable energy and Lyapunov functionals, we establish a general decay estimate for the energy, which depends on the behavior of both <TEX>${\sigma}$</TEX> and g.