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September, 2010 Aronson-Bénilan type estimate and the optimal Hölder continuity of weak solutions for the 1-D degenerate Keller-Segel systems
Yoshie Sugiyama
Rev. Mat. Iberoamericana 26(3): 891-913 (September, 2010).

Abstract

We consider the Keller-Segel system of degenerate type (KS)$_m$ with $m > 1$below. We establish a uniform estimate of $\partial_x^2 u^{m-1}$ from below.The corresponding estimate to the porous medium equation is well-knownas an Aronson-Bénilan type. We apply our estimate to provethe optimal Hölder continuity of weak solutions of (KS)$_m$.In addition, we find that the set $D(t):=\{ x \in \mathbb{R}; u(x,t) > 0\}$ of positive region to the solution $u$ is monotonically non-decreasing with respect to $t$.

Citation

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Yoshie Sugiyama . "Aronson-Bénilan type estimate and the optimal Hölder continuity of weak solutions for the 1-D degenerate Keller-Segel systems." Rev. Mat. Iberoamericana 26 (3) 891 - 913, September, 2010.

Information

Published: September, 2010
First available in Project Euclid: 27 August 2010

zbMATH: 1213.35154
MathSciNet: MR2789369

Subjects:
Primary: 35B57, 35K45, 35K55, 35K65

Rights: Copyright © 2010 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.26 • No. 3 • September, 2010
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