Differential and Integral Equations

Finite time blow-up of the solution for a nonlinear parabolic equation of drift-diffusion type

Masaki Kurokiba and Takayoshi Ogawa

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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].

Article information

Source
Differential Integral Equations, Volume 16, Number 4 (2003), 427-452.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060652

Mathematical Reviews number (MathSciNet)
MR1972874

Zentralblatt MATH identifier
1161.35432

Subjects
Primary: 35K57: Reaction-diffusion equations
Secondary: 35B40: Asymptotic behavior of solutions

Citation

Kurokiba, Masaki; Ogawa, Takayoshi. Finite time blow-up of the solution for a nonlinear parabolic equation of drift-diffusion type. Differential Integral Equations 16 (2003), no. 4, 427--452. https://projecteuclid.org/euclid.die/1356060652


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