Existence and energy decay rates of solutions to the variable-coefficient Euler–Bernoulli plate with a delay in localized nonlinear internal feedback

Abstract

This paper is concerned with the existence and energy decay estimates of solutions to the variable-coefficient Euler–Bernoulli plate with a delay in localized nonlinear internal feedback. The existence of solutions to the nonlinear system is obtained by using Galerkin method combined with some energy estimates. Furthermore, applying Riemannian geometry method, we establish uniform decay rates of the plate equation with variable coefficients and a nonlinear delay term.