Math. Model. Nat. Phenom.
Volume 11, Number 2, 2016Spectral problems
|Page(s)||44 - 62|
|Published online||21 March 2016|
Eigenfunction Approach to Transient Patterns in a Model of Chemotaxis
Institute of Fundamental Technological Research Polish Academy of Sciences
⋆ Corresponding author. E-mail: firstname.lastname@example.org
In the paper we examine solutions to a model of cell movement governed by the chemotaxis phenomenon derived in  and established via macroscopic limits of corresponding microscopic cell-based models with extended cell representations. The model is given by two PDEs for the density of cells and the concentration of a chemical. To avoid singularities in cell density, the aggregating force of chemotaxis phenomenon is attenuated by a density dependent diffusion of cells, which grows to infinity with density tending to a certain critical value. In this paper we recover the quasi-periodic structures provided by this model by means of (local in time) expansion of the solution into a basis of eigenfunctions of the linearized system. Both planar and spherical geometries are considered.
Mathematics Subject Classification: 35B36 / 35B20 / 35B32 / 65N25 / 65P30
Key words: pattern formation / chemotaxis / Turing bifurcation / eigenfunction expansion
© EDP Sciences, 2016
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