The lifespan of solutions for a viscoelastic wave equation with a strong damping and logarithmic nonlinearity

Abstract

<p style='text-indent:20px;'>This paper deals with the following viscoelastic wave equation with a strong damping and logarithmic nonlinearity:</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ u_{tt}-\Delta u+\int_0^tg(t-s)\Delta u(s)ds-\Delta u_t = |u|^{p-2}u\ln|u|. $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>A finite time blow-up result is proved for high initial energy. Meanwhile, the lifespan of the weak solution is discussed. The present results in this paper complement and improve the previous work that is obtained by Ha and Park [<i>Adv. Differ. Equ.</i>, (2020) 2020: 235].</p>