Blowup rate estimates for the heat equation with a nonlinear gradient source term
Jong-Shenq Guo - Department of Mathematics, National Taiwan Normal University, 88, S-4, Ting Chou Road, Taipei 11677, Taiwan (email)
Abstract: 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.
Keywords: gradient blowup, blowup rate, nonlinear gradient source.
Received: March 2007; Revised: September 2007; Published: January 2008.
2011 Impact Factor.913