A study of blow-ups in the Keller–Segel model of chemotaxis

DOI10.1088/0951-7715/26/1/81zbMath1322.35057arXiv1006.4978OpenAlexW3104257744MaRDI QIDQ4920052

Ibrahim Fatkullin

Publication date: 16 May 2013

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.4978

zbMATH Keywords

singularitieschemotaxisKeller-Segel modelparticle-grid numerical method

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Cell movement (chemotaxis, etc.) (92C17) Blow-up in context of PDEs (35B44) Initial-boundary value problems for second-order parabolic systems (35K51) Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs (65M75)

Related Items (12)

Third order positivity-preserving direct discontinuous Galerkin method with interface correction for chemotaxis Keller-Segel equations ⋮ Numerical investigation of chemotaxic phenomenon in incompressible viscous fluid flow ⋮ A meshless technique based on the local radial basis functions collocation method for solving parabolic-parabolic Patlak-Keller-Segel chemotaxis model ⋮ Linear energy stable numerical schemes for a general chemo-repulsive model ⋮ An unconditionally energy stable and positive upwind DG scheme for the Keller-Segel model ⋮ Local discontinuous Galerkin method for the Keller-Segel chemotaxis model ⋮ Traveling waves for the Keller-Segel-FKPP equation with strong chemotaxis ⋮ Blow-up dynamics for the aggregation equation with degenerate diffusion ⋮ Exact traveling wave solutions of one-dimensional parabolic-parabolic models of chemotaxis ⋮ Energy dissipative local discontinuous Galerkin methods for Keller-Segel chemotaxis model ⋮ An analysis on the finite volume schemes and the discrete Lyapunov inequalities for the chemotaxis system ⋮ A new numerical method to solve some \(\mathrm{PDE_s}\) in the unit ball and comparison with the finite element and the exact solution

Uses Software

• Chemotaxis

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