Lower bounds for the blowup time of solutions to a nonlinear parabolic problem
Haixia Li, Wenjie Gao, Yuzhu Han · DOAJ (DOAJ: Directory of Open Access Journals) · 2014
In this short article, we study the blow-up properties of solutions to a parabolic problem with a gradient nonlinearity under homogeneous Dirichlet boundary conditions. By constructing an auxiliary function and by modifying the first order differential inequality technique introduced by Payne et al., we obtain a lower bound for the blow-up time of solutions in a bounded domain $\Omega\subset \mathbb{R}^n$ for any $n\geq3$. This article generalizes a result in [16].