Chipot, M.; Weissler, F. B. Some blowup results for a nonlinear parabolic equation with a gradient term. (English) Zbl 0682.35010 SIAM J. Math. Anal. 20, No. 4, 886-907 (1989). This paper concerns the blow-up in finite time of solutions of semilinear parabolic initial-boundary value problems on bounded domains in \({\mathbb{R}}^ N\), when the nonlinear term has gradient dependence. The gradient term has a damping effect, working against blow-up, but nevertheless it is shown for a simple model equation that blow-up in finite time occurs, under some technical assumptions, in the supremum norm. Reviewer: J.Toland Cited in 5 ReviewsCited in 83 Documents MSC: 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 35K55 Nonlinear parabolic equations 35B35 Stability in context of PDEs Keywords:gradient dependent nonlinearity; blow-up PDF BibTeX XML Cite \textit{M. Chipot} and \textit{F. B. Weissler}, SIAM J. Math. Anal. 20, No. 4, 886--907 (1989; Zbl 0682.35010) Full Text: DOI Link OpenURL