Existence of global solutions of a macroscopic model of cellular motion in a chemotactic field

DOI10.1016/j.aml.2009.05.013zbMath1176.35098OpenAlexW2066694221MaRDI QIDQ1036806

Richard Gejji, Mark S. Alber, Bogdan Kaźmierczak

Publication date: 13 November 2009

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2009.05.013

zbMATH Keywords

reaction-diffusion systemsglobal existencenonlinear diffusioncontinuous limitdiscrete cellular Potts model

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Cell movement (chemotaxis, etc.) (92C17) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (8)

Eigenfunction Approach to Transient Patterns in a Model of Chemotaxis ⋮ Classification and stability of global inhomogeneous solutions of a macroscopic model of cell motion ⋮ Global existence to an attraction-repulsion chemotaxis model with fast diffusion and nonlinear source ⋮ Model of chemotaxis with threshold density and singular diffusion ⋮ Global existence and blow up of solutions of quasilinear chemotaxis system ⋮ Initial-boundary value problems for a system of hyperbolic balance laws arising from chemotaxis ⋮ Mathematical modelling of atherosclerosis ⋮ Existence of a nontrivial steady-state solution to a parabolic-parabolic chemotaxis system with singular sensitivity

Cites Work

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• Dynamic theory of quasilinear parabolic equations. II: Reaction-diffusion systems
• Dynamic theory of quasilinear parabolic systems. III: Global existence
• Model of chemotaxis with threshold density and singular diffusion
• Prevention of blow-up by fast diffusion in chemotaxis
• Biased random walk models for chemotaxis and related diffusion approximations
• Singularity patterns in a chemotaxis model
• Classical solutions and pattern formation for a volume filling chemotaxis model
• Diffusion, attraction and collapse
• Aggregation, Blowup, and Collapse: The ABC's of Taxis in Reinforced Random Walks

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