Immediate smoothing and global solutions for initial data in L¹× W^1,2 in a Keller-Segel system with logistic terms in 2D

2020/03/05 by Johannes Lankeit, Lankeit, Johannes
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #35A09 #35B65 (primary) #35K45 #35Q92 #92C17 #Analysis of PDEs (math.AP) #Cancer Cells and Metastasis #FOS: Mathematics #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth

paper · pdf · doi:10.48550/arxiv.2003.02644

openalex publication_date 2020/03/05 · openalex created_date 2020/03/13 · openalex updated_date 2026/07/28

Abstract

This article deals with the logistic Keller-Segel model \begincases u_t = Δu - χ∇⋅(u∇ v) + κu - μu²,

v_t = Δv - v + u \endcases in bounded two-dimensional domains (with homogeneous Neumann boundary conditions and for parameters χ, κ∈ ℝ and μ>0), and shows that any nonnegative initial data (u₀,v₀)∈ L¹× W^1,2 lead to global solutions that are smooth in Ω×(0,∞).

Citations

• On explosions of solutions to a system of partial differential equations modelling chemotaxis
• Aggregation vs. global diffusive behavior in the higher-dimensional Keller–Segel model

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