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October  2008, 20(4): 927-937. doi: 10.3934/dcds.2008.20.927

Blowup rate estimates for the heat equation with a nonlinear gradient source term

1. 

Department of Mathematics, National Taiwan Normal University, 88, S-4, Ting Chou Road, Taipei 11677, Taiwan

2. 

Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556

Received  March 2007 Revised  September 2007 Published  January 2008

The gradient blowup rate of the equation $u_t = \Delta u + |\nabla u|^p$, where $p>2$, is studied. It is shown that the blowup rate will never match that of the self-similar variables. In the one space dimensional case when assumptions are made on the initial data so that the solution is monotonically increasing in time, the exact blowup rate is found.
Citation: Jong-Shenq Guo, Bei Hu. Blowup rate estimates for the heat equation with a nonlinear gradient source term. Discrete & Continuous Dynamical Systems - A, 2008, 20 (4) : 927-937. doi: 10.3934/dcds.2008.20.927
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