Global existence of solutions to a parabolic-elliptic chemotaxis system with critical degenerate diffusion

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:417

Article

Nasreddine, Elissar

关键词: Chemotaxis;    Keller-Segel model;    Parabolic equation;    Elliptic equation;    Global existence;    Uniqueness;   

DOI  :  10.1016/j.jmaa.2014.02.069

来源: Elsevier

【 摘 要 】

This paper is devoted to the analysis of nonnegative solutions for a degenerate parabolic elliptic Patlak-Keller-Segel system with critical nonlinear diffusion in a bounded domain with homogeneous Neumann boundary conditions. Our aim is to prove the existence of a global weak solution under a smallness condition on the mass of the initial data, thereby completing previous results on finite blow-up for large masses. Under some higher regularity condition on solutions, the uniqueness of solutions is proved by using a classical duality technique. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free