May/June 2014 Existence and blowing up for a system of the drift-diffusion equation in $R^2$
Masaki Kurokiba
Differential Integral Equations 27(5/6): 425-446 (May/June 2014). DOI: 10.57262/die/1396558090

Abstract

We discuss the existence of the blow-up solution for multi-component parabolic-elliptic drift-diffusion model in two space dimensions. We show that the local existence, uniqueness and well posedness of a solution in the weighted $L^2$ spaces. Moreover, we prove 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 and drift-diffusion equation proved by Nagai [22] and Nagai-Senba-Suzuki [24] and gravitational interaction of particles by Biler-Nadzieja [4], [5]. We generalize the result in Kurokiba-Ogawa [17] for multi-component problem and give a sufficient condition for the finite time blow up of the solution.

Citation

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Masaki Kurokiba. "Existence and blowing up for a system of the drift-diffusion equation in $R^2$." Differential Integral Equations 27 (5/6) 425 - 446, May/June 2014. https://doi.org/10.57262/die/1396558090

Information

Published: May/June 2014
First available in Project Euclid: 3 April 2014

zbMATH: 1340.35121
MathSciNet: MR3189526
Digital Object Identifier: 10.57262/die/1396558090

Subjects:
Primary: 35K15 , 35K55 , 35Q60 , 78A35

Rights: Copyright © 2014 Khayyam Publishing, Inc.

Vol.27 • No. 5/6 • May/June 2014
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