The Patlak-Keller-Segel model and its variations: properties of solutions via maximum principle

2011/02/01 by Inwon Kim, Yao Yao, Kim, Inwon +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth #advanced mathematical theories #math.AP

paper · pdf · doi:10.48550/arxiv.1102.0092

revised version, to appear in SIAM J. on Mathematical Analysis

openalex publication_date 2011/02/01 · arxiv created 2011/11/10 · arxiv updated 2011/11/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper we investigate qualitative and asymptotic behavior of solutions for a class of diffusion-aggregation equations. Most results except the ones in section 3 and 6 concern radial solutions. The challenge in the analysis consists of the nonlocal aggregation term as well as the degeneracy of the diffusion term which generates compactly supported solutions. The key tools used in the paper are maximum-principle type arguments as well as estimates on mass concentration of solutions.

Citations

• Model for chemotaxis
• Stationary states of quadratic diffusion equations with long-range attraction

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