Some blowup results for a nonlinear parabolic equation with a gradient term. (English) Zbl 0682.35010

Chipot, M.; Weissler, F. B.

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

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