Decay estimate in a viscoelastic plate equation with past history, nonlinear damping, and logarithmic nonlinearity

TL;DR

This paper establishes explicit decay rates for solutions to a viscoelastic plate equation incorporating past history, nonlinear damping, and logarithmic nonlinearity, using convexity and inequality techniques.

Contribution

It provides new explicit decay estimates for a complex viscoelastic plate model with nonlinear and historical effects.

Findings

Proved explicit decay rates for solutions.

Utilized convex properties and inequalities in proofs.

Enhanced understanding of long-term behavior of viscoelastic plates.

Abstract

In this article, we consider a viscoelastic plate equation with past history, nonlinear damping, and logarithmic nonlinearity. We prove explicit and general decay rate results of the solution to the viscoelastic plate equation with past history. Convex properties, logarithmic inequalities, and generalised Young's inequality are mainly used to prove the decay estimate.