Lower and upper bounds for the blow-up time for a thin-film equation with variable exponent in the reaction term
Volume 129 / 2022
Annales Polonici Mathematici 129 (2022), 55-76
MSC: Primary 35B44; Secondary 35K15, 35K05, 35K57.
DOI: 10.4064/ap210309-27-4
Published online: 20 July 2022
Abstract
This paper deals with the blow-up phenomena for solutions to a thin-film equation with a variable exponent in the reaction term. We consider the case where the initial energy is positive to obtain a lower bound for blow-up results if blow-up occurs for this case. We give a new blow-up criterion, and under some conditions on $p(\cdot )$ and $u_{0}$ we establish the lifespan $\widehat T$ of the solution. The blow-up time with negative initial energy is also derived.
