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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
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