Energy decay of dissipative plate equations with memory-type boundary conditions

Abstract

Abstract. In this paper we consider a plate equation with internal feedback and viscoelastic damping localized on a part of the boundary. Without imposing restrictive assumptions on the time-dependent frictional damping, we establish an explicit and general decay rate result that allows a wider class of relaxation functions and generalizes previous results existing in the literature.

Optimal decay result for Kirchhoff plate equations with nonlinear damping and very general type of relaxation functions

“…In [34], Lasiecka et al established optimal decay rate for all 1 ≤ p < 2, but with γ (t) = 1. Very recently, Mustafa [39] obtained optimal exponential and polynomial decay rates for all 1 ≤ p < 2 and γ is a function of t. The work most closely related to our study is by Kang [40], Mustafa and Abusharkh [41] and Mustafa [42]. Kang [40] investigated the system (1)- (5) whereas η(t) ≡ 1 and…”

“…They established explicit and general decay rate results. Very recently, Mustafa [42] studied system (1)- (5). However, under the same condition (9) he obtained a general decay rate result.…”

“…Our contribution in this paper is to investigate the system (1)-(5) under a very general assumption on the resolvent kernels r i . This assumption is more general as it comprises the earlier results in [40,41] and [42] in the presence of ξ (t) and the very general assumption on the relaxation functions. Furthermore, we obtain our results without imposing any restrictive growth assumption on the damping and take into account the effect of the time-dependent coefficient η(t).…”