Stability result of a viscoelastic plate equation with past history and a logarithmic nonlinearity

Abstract

AbstractIn this paper, we are concerned with the decay rate of the solution of a viscoelastic plate equation with infinite memory and logarithmic nonlinearity. We establish an explicit and general decay rate results with imposing a minimal condition on the relaxation function. In fact, we assume that the relaxation function h satisfies $$ h^{\prime}(t)\le-\xi(t) H\bigl(h(t)\bigr),\quad t\geq0, $$h′(t)≤−ξ(t)H(h(t)),t≥0, where the functions ξ and H satisfy some conditions. Our proof is based on the multiplier method, convex properties, logarithmic inequalities, and some properties of integro-differential equations. Moreover, we drop the boundedness assumption on the history data, usually made in the literature. In fact, our results generalize, extend, and improve earlier results in the literature.