Uniqueness and convergence on equilibria of the Keller-Segel system with subcritical mass

2018/04/10 by Jun Wang, Wang, Jun, Zhi‐An Wang +3 · 2 citations
Mathematics · Biochemistry, Genetics and Molecular Biology · Medicine · #Mathematical Biology Tumor Growth #Gene Regulatory Network Analysis #Cancer Cells and Metastasis

paper · pdf · doi:10.48550/arxiv.1804.03319

Abstract

This paper is concerned with the uniqueness of solutions to the following nonlocal semi-linear elliptic equation Δu-βu+λ(e^u)/(∫_Ωe^u)=0~in~Ω, where Ω is a bounded domain in ℝ² and β, λ are positive parameters. The above equation arises as the stationary problem of the well-known classical Keller-Segel model describing chemotaxis. For equation \eqrefellip with Neumann boundary condition, we establish an integral inequality and prove that the solution of (\refellip) is unique if 0

Citations

• A user’s guide to PDE models for chemotaxis

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