Holder regularity and uniqueness theorem on weak solutions to the degenerate Keller-Segel system

被引：8

作者：

Kim, Sunghoon ^{[1
]}

Lee, Ki-Ahm ^{[2
,3
]}

机构：

[1] Catholic Univ Korea, Sch Nat Sci, Dept Math, 43 Jibong Ro, Bucheon Si 420743, Gyeonggi Do, South Korea

[2] Seoul Natl Univ, Sch Math Sci, Seoul 151747, South Korea

[3] Korea Inst Adv Study, Ctr Math Challenges, Seoul 130722, South Korea

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2016年 / 138卷

基金：

新加坡国家研究基金会;

关键词：

Degenerate Keller-Segel system; Holder estimate; Uniqueness; SINGULAR PARABOLIC EQUATIONS; POROUS-MEDIUM EQUATION; GLOBAL EXISTENCE; CHEMOTAXIS SYSTEM; SMOOTH SOLUTION; BOUNDED DOMAIN; OPERATORS; BEHAVIOR; MODEL; MASS;

D O I：

10.1016/j.na.2015.11.024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present local Holder estimates for the degenerate Keller-Segel system (KSm) below in the range of m > 1 and q > 2 before a blow-up of solutions. To deal with difficulties caused by the degeneracy of the operator, we find uniform estimates depending on sup-norm of the density function and modified the energy estimates and intrinsic scales considered in Porous Medium Equation. As its application, the uniqueness of weak solution to (KSm) is also showed for the case q > max (1 + m/2, 2) in the class of Holder continuous functions by proving L-1-contraction in this class. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：229 / 252

页数：24

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