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Zbl 1159.35009
Guo, Jong-Sheng; Hu, Bei
Blowup rate estimates for the heat equation with a nonlinear gradient source term. (English)
[J] Discrete Contin. Dyn. Syst. 20, No. 4, 927-937 (2008). ISSN 1078-0947; ISSN 1553-5231/e

A semilinear parabolic equation with a superquadratic gradient term is considered. A lower bound for the rate of blow-up of the gradient is established. The corresponding upper bound is shown to hold in one space-dimension for solutions which increase in time. In particular, the blow-up rate is never self-similar.
[Marek Fila (Bratislava)]
MSC 2000:
*35B40 Asymptotic behavior of solutions of PDE
35K55 Nonlinear parabolic equations

Keywords: gradient blow-up; blow-up rate; superquadratic gradient term

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