Abstract
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.
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Acknowledgments
The authors would like to thank the anonymous referees for their valuable comments, which greatly improved the exposition of the paper.
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The work was partially supported by the National Natural Science Foundation of China (11671359), the Provincial Natural Science Foundation of Zhejiang (LY15A010017, LY16A010009), and the Science Foundation of Zhejiang Sci-Tech University 15062173-Y.
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Ma, Mj., Li, H., Gao, My. et al. Traveling wavefronts for a reaction-diffusion-chemotaxis model with volume-filling effect. Appl. Math. J. Chin. Univ. 32, 108–116 (2017). https://doi.org/10.1007/s11766-017-3409-4
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DOI: https://doi.org/10.1007/s11766-017-3409-4