Numerical and Theoretical Stability Study of a Viscoelastic Plate Equation with Nonlinear Frictional Damping Term and a Logarithmic Source Term

Abstract

This paper is designed to explore the asymptotic behaviour of a two dimensional visco-elastic plate equation with a logarithmic nonlinearity under the influence of nonlinear frictional damping. Assuming that relaxation function g satisfies g′(t)≤−ξ(t)G(g(t)), we establish an explicit general decay rates without imposing a restrictive growth assumption on the damping term. This general condition allows us to recover the exponential and polynomial rates. Our results improve and extend some existing results in the literature. We preform some numerical experiments to illustrate our theoretical results.