Geodesic
Eigenfunction Approach to Transient Patterns in a Model of Chemotaxis
P. Chatterjee1 ; B. Kazmierczak1
1 Institute of Fundamental Technological Research Polish Academy of Sciences
Mathematical modelling of natural phenomena, Tome 11 (2016) no. 2, pp. 44-62

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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.
DOI : 10.1051/mmnp/201611204

P. Chatterjee 1 ; B. Kazmierczak 1

1 Institute of Fundamental Technological Research Polish Academy of Sciences 
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P. Chatterjee; B. Kazmierczak. Eigenfunction Approach to Transient Patterns in a Model of Chemotaxis. Mathematical modelling of natural phenomena, Tome 11 (2016) no. 2, pp. 44-62. doi: 10.1051/mmnp/201611204

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