Electron. J. Diff. Equ., Vol. 2014 (2014), No. 20, pp. 1-6.

Lower bounds for the blowup time of solutions to a nonlinear parabolic problem

Haixia Li, Wenjie Gao, Yuzhu Han

Abstract:
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].

Submitted December 20, 2013. Published January 10, 2014.
Math Subject Classifications: 35K58, 35B44.
Key Words: Blow-up time; lower bounds; gradient nonlinearity.

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Haixia Li
School of Mathematics, Jilin University
Changchun 130012, China
email: lihaixia0611@126.com
Wenjie Gao
School of Mathematics, Jilin University
Changchun 130012, China
email: wjgao@jlu.edu.cn
Yuzhu Han
School of Mathematics, Jilin University
Changchun 130012, China
email: yzhan@jlu.edu.cn}

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