On a viscoelastic heat equation with logarithmic nonlinearity

Abstract

This work deals with the following viscoelastic heat equations with logarithmic nonlinearity \begin{align*} u_t-\Delta u+\int_{0}^{t}g(t-s)\Delta u(s)ds=\vert u\vert^{p-2}u\ln\vert u\vert. \end{align*} In this paper, we show the effects of the viscoelastic term and the logarithmic nonlinearity to the asymptotic behavior of weak solutions. Our results extend the results of Peng and Zhou [Appl. Anal. 100(2021), 2804–2824] and Messaoudi [Nonlinear Differ. Equ. Appl. 64(2005), 351–356].

Keywords

• viscoelastic heat equation
• global existence
• blow-up
• blow-up time
• exponential decay
• logarithmic nonlinearity