Traveling wavefronts for a reaction-diffusion-chemotaxis model with volume-filling effect

In this paper, we study the propagation of the pattern for a reaction-diffusionchemotaxis model. By using a weakly nonlinear analysis with multiple temporal and spatial scales, we establish the amplitude equations for the patterns, which show that a local perturbation at the constant steady state is...

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Bibliographic Details
Published inApplied Mathematics-A Journal of Chinese Universities Vol. 32; no. 1; pp. 108 - 116
Main Authors Ma, Man-jun, Li, Hui, Gao, Mei-yan, Tao, Ji-cheng, Han, Ya-zhou
Format Journal Article
LanguageEnglish
Published Hangzhou Editorial Committee of Applied Mathematics - A Journal of Chinese Universities 01.03.2017
Springer Nature B.V
Subjects
Applications of Mathematics
Computer simulation
Mathematical models
Mathematics
Mathematics and Statistics
Nonlinear analysis
Perturbation methods
Wave fronts
chemotaxis model
traveling wavefront
weakly nonlinear analysis
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Summary:In this paper, we study the propagation of the pattern for a reaction-diffusionchemotaxis model. By using a weakly nonlinear analysis with multiple temporal and spatial scales, we establish the amplitude equations for the patterns, which show that a local perturbation at the constant steady state is spread over the whole domain in the form of a traveling wavefront. The simulations demonstrate that the amplitude equations capture the evolution of the exact patterns obtained by numerically solving the considered system.
ISSN:1005-1031
1993-0445
DOI:10.1007/s11766-017-3409-4