Abstract
The main goal of this paper is to study for the local existence and decay estimates results for a high-order viscoelastic wave equation with logarithmic nonlinerity. We obtain several results: Firstly, by using Feado-Galerkin method and a logaritmic Sobolev inequality, we proved local existence of solutions. Later, we proved general decay results of solutions.
Highlights
We investigate the following nonlinear initial boundary value problem
The equation with the logarithmic source term is related with many branches of physics
We give some notations and lemmas and preliminary results in order to state the main results of this paper
Summary
We investigate the following nonlinear initial boundary value problem. The equation with the logarithmic source term is related with many branches of physics. Cause of this is interest in it occures naturally in in‡ation cosmology and supersymmetric ...eld theories, quantum mechanics, nuclear physics [6, 8, 9]. : He studied the decay estimate and exponential growth of solutions for the problem (3). We established the local existence, and general decay estimates of the solution for problem (1).
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