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Finite Time Blow-up for a Non-linear Parabolic Equation with a Gradient Term and Applications (1996)

Souplet, Philippe

Chichester, West Sussex : Wiley-Blackwell

Mathematical Methods in the Applied Sciences 19 (1996), S. 1317-1333

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ISSN: 0170-4214

Keywords: Engineering ; Numerical Methods and Modeling

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Mathematics

Notes: We give new finite time blow-up results for the non-linear parabolic equations ut-Δu = up and ut-Δu+μ∣∇u∣q = up. We first establish an a priori bound in Lp+1 for the positive non-decreasing global solutions. As a consequence, we prove in particular that for the second equation on ∝N, with q = 2p/(p+1) and small μ〉0, blow-up can occur for any N≥1, p〉1, (N-2)p〈N+2 and without energy restriction on the initial data. Incidentally, we present a simple model in population dynamics involving this equation.

Type of Medium: Electronic Resource

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