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On finite-time blow-up for a nonlocal parabolic problem arising from shear bands in metals

Author: Gao-Feng Zheng
Journal: Proc. Amer. Math. Soc. 135 (2007), 1487-1494
MSC (2000): Primary 35K10, 35K57, 35K60.
Published electronically: November 27, 2006
MathSciNet review: 2276658
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Abstract: Results on finite-time blow-up of solutions to the nonlocal parabolic problem

\begin{displaymath} \left\{ \begin{array}{ll} u_t=\Delta u +\delta \displaystyle... ...\\ u(x,0)=u_0(x)\geqslant 0,& x\in \Omega \end{array}\right. \end{displaymath}

are established. They extend some known results to higher dimensions.

References [Enhancements On Off] (What's this?)

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Additional Information

Gao-Feng Zheng
Affiliation: Department of Mathematics, Huazhong Normal University, Wuhan, People’s Republic of China

Keywords: Nonlocal parabolic equations, finite-time blow-up, method of moving planes.
Received by editor(s): October 5, 2005
Received by editor(s) in revised form: December 20, 2005
Published electronically: November 27, 2006
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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