Lifespan of solutions to a damped plate equation with logarithmic nonlinearity
Yuzhu Han, Qi Li
Abstract
<p style='text-indent:20px;'>This paper is devoted to the lifespan of solutions to a damped plate equation with logarithmic nonlinearity</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ u_{tt}+\Delta^2u-\Delta u-\Delta u_t+u_t = |u|^{p-2}u\ln|u|. $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>Finite time blow-up criteria for solutions at both lower and high initial energy levels are established and an upper bound for the blow-up time is given for each case. Moreover, by constructing a new auxiliary functional and making full use of the strong damping term, a lower bound for the blow-up time is also derived.</p>