Well-posedness of a model of point dynamics for a limit of the Keller-Segel system

DOI10.1016/j.jde.2004.05.013zbMath1063.35068OpenAlexW2007850214MaRDI QIDQ703818

Juan J. L. Velazquez

Publication date: 11 January 2005

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2004.05.013

zbMATH Keywords

singularitiesfixed point theoremfree boundary problems

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Cell movement (chemotaxis, etc.) (92C17) Second-order parabolic systems (35K40)

Related Items (9)

STATISTICAL MODELS OF CRIMINAL BEHAVIOR: THE EFFECTS OF LAW ENFORCEMENT ACTIONS ⋮ LOCAL EXISTENCE AND UNIQUENESS OF SOLUTIONS TO A PDE MODEL FOR CRIMINAL BEHAVIOR ⋮ On a parabolic-elliptic system with chemotaxis and logistic type growth ⋮ Stochastic particle approximation for measure valued solutions of the 2D Keller-Segel system ⋮ A STATISTICAL MODEL OF CRIMINAL BEHAVIOR ⋮ Existence, uniqueness and Lipschitz dependence for Patlak-Keller-Segel and Navier-Stokes in \(\mathbb R^2\) with measure-valued initial data ⋮ Generalized Global Supersolutions with Mass Control for Systems with Taxis ⋮ Convergence of a Stochastic Particle Approximation for Measure Solutions of the 2D Keller-Segel System ⋮ The steady states and convergence to equilibria for a 1-D chemotaxis model with volume-filling effect

Cites Work

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• Diffusion, attraction and collapse
• Point Dynamics in a Singular Limit of the Keller--Segel Model 1: Motion of the Concentration Regions
• Point Dynamics in a Singular Limit of the Keller--Segel Model 2: Formation of the Concentration Regions
• Chemotactic collapse in a parabolic system of mathematical biology
• The nonsymmetric case of the Keller-Segel model in chemotaxis: some recent results.

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