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2003 Finite time blow-up of the solution for a nonlinear parabolic equation of drift-diffusion type
Masaki Kurokiba, Takayoshi Ogawa
Differential Integral Equations 16(4): 427-452 (2003).

Abstract

We discuss the existence of the blow-up solution for some nonlinear parabolic system called attractive drift-diffusion equation in two space dimensions. We show that if the initial data satisfies a threshold condition, the corresponding solution blows up in a finite time. This is a system case for the blow-up result of the chemotactic equation proved by Nagai [28] and Nagai-Senba-Suzuki [30] and gravitational interaction of particles by Biler-Nadzieja [7], [8].

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Masaki Kurokiba. Takayoshi Ogawa. "Finite time blow-up of the solution for a nonlinear parabolic equation of drift-diffusion type." Differential Integral Equations 16 (4) 427 - 452, 2003.

Information

Published: 2003
First available in Project Euclid: 21 December 2012

zbMATH: 1161.35432
MathSciNet: MR1972874

Subjects:
Primary: 35K57
Secondary: 35B40

Rights: Copyright © 2003 Khayyam Publishing, Inc.

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Vol.16 • No. 4 • 2003
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