Bounds for blow-up time in a semilinear parabolicproblem with variable exponents

Abstract

This report deals with a blow-up of the solutions to a class of semilinear parabolic equations with variable exponents nonlinearities. Under some appropriate assumptions on the given data, a more general lower bound for a blow-up time is obtained if the solutions blow up. This result extends the recent results given by Baghaei Khadijeh et al. \cite{Baghaei}, which ensures the lower bounds for the blow-up time of solutions with initial data $\varphi\left( 0\right) =\int_{\Omega }u_{0}{}^{k}dx$, $k$ = constant.