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

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