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2008 Asymptotic stability of a decaying solution to the Keller-Segel system of degenerate type
Takayoshi Ogawa
Differential Integral Equations 21(11-12): 1113-1154 (2008).

Abstract

We discuss the global behavior of the weak solution of the Keller-Segel system of degenerate type. Asymptotic stability of the Barenblatt-Pattle solution and its convergence rate for the decaying weak solution in $L^1({\mathbb R}^n)$ is shown for the degenerated case $1 <{\alpha} < 2-\frac{2}{n}$. The method is based on the techniques applied to the Fokker-Plank equation due to Carrillo-Toscani [8] deriving from the explicit time decay of the free energy functional and some new estimates for the nonlinear interaction involving the critical type Sobolev inequality. We give the rigorous justification of those procedures via some approximating procedures.

Citation

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Takayoshi Ogawa. "Asymptotic stability of a decaying solution to the Keller-Segel system of degenerate type." Differential Integral Equations 21 (11-12) 1113 - 1154, 2008.

Information

Published: 2008
First available in Project Euclid: 14 December 2012

zbMATH: 1224.35229
MathSciNet: MR2482499

Subjects:
Primary: 35M31
Secondary: 35B35, 35K65

Rights: Copyright © 2008 Khayyam Publishing, Inc.

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Vol.21 • No. 11-12 • 2008
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