General decay of a nonlinear viscoelastic wave equation with the logarithmic nonlinearity, not necessarily decreasing kernel and acoustic boundary conditions

Dandan Guo; ZHIFEI ZHANG

doi:10.22541/au.171928921.11588348/v1

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General decay of a nonlinear viscoelastic wave equation with the logarithmic nonlinearity, not necessarily decreasing kernel and acoustic boundary conditions

Dandan Guo,
ZHIFEI ZHANG

Abstract

In this work we investigate a viscoelastic wave equation involving a logarithmic nonlinearity and acoustic boundary conditions. Making some assumptions on the memory kernel function g, which is not necessarily decreasing and using Lyapunov method, we establish a general decay estimate of the solution.