Exponential stability for a plate equation with p‐Laplacian and memory terms

Abstract

This paper is concerned with the energy decay for a class of plate equations with memory and lower order perturbation of p-Laplacian type,with simply supported boundary condition, where is a bounded domain of R N , g > 0 is a memory kernel that decays exponentially and f .u/ is a nonlinear perturbation. This kind of problem without the memory term models elastoplastic flows.A more general equation,

STABILITY FOR A VISCOELASTIC PLATE EQUATION WITH p-LAPLACIAN

“…The results of this article extend those of [1] with respect to some aspects. The plan of this paper is as follows.…”

“…and proved a general decay result which depends both on the behavior of σ and g. Inspired by [1,7], we investigate the general decay estimate of solutions for the weak viscoelastic beam equation with p-Lapalcian. The results of this article extend those of [1] with respect to some aspects.…”

“…On the other hand, Andrade et al [1] discussed the energy decay of solutions for problem (1.1)-(1.3) when σ(t) = 1. The interaction of the memory term with p-Laplacian operator was first considered by them.…”

General decay for viscoelastic plate equation with p-Laplacian and time-varying delay

“…Then using elliptic regularity and second order estimates we can show the regularity of the solution. We state a well-posedness result without a proof here (see [6,7,13,17]). …”

“…Andrade et al [7] proved exponential stability of solutions for the plate equation with finite memory and p-Laplacian. The viscosity term -u t is often called a Kelvin-Voigt type dissipation or strong dissipation; it appears in phenomena of wave propagation in a viscoelastic material.…”