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
for any
.
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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