GRADIENT ESTIMATE FOR SOLUTIONS TO QUASILINEAR NON-DEGENERATE KELLER-SEGEL SYSTEMS ON RN

被引：3

作者：

Ishida, Sachiko ^{[1
]}

Maeda, Yusuke ^{[1
]}

Yokota, Tomomi ^{[1
]}

机构：

[1] Tokyo Univ Sci, Dept Math, Shinjuku Ku, Tokyo 1628601, Japan

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2013年 / 18卷 / 10期

基金：

日本学术振兴会;

关键词：

Quasilinear non degenerate Keller-Segel systems; blow-up; GLOBAL EXISTENCE; PARABOLIC-SYSTEMS;

D O I：

10.3934/dcdsb.2013.18.2537

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper gives the gradient estimate for solutions to the quasilinear non-degenerate parabolic-parabolic Keller-Segel system (KS) on the whole space R-N. The gradient estimate for (KS) on bounded domains is known as an application of Amann's existence theory in [1]. However, in the whole space case it seems necessary to derive the gradient estimate directly. The key to the proof is a modified Bernstein's method. The result is useful to obtain the whole space version of the global existence result by Tao-Winkler [13] except for the boundedness.

引用

页码：2537 / 2568

页数：32

共 13 条

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