Traveling wavefronts for a reaction-diffusion-chemotaxis model with volume-filling effect
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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.
Keywordschemotaxis model traveling wavefront weakly nonlinear analysis
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The authors would like to thank the anonymous referees for their valuable comments, which greatly improved the exposition of the paper.