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

  • Man-jun Ma
  • Hui Li
  • Mei-yan Gao
  • Ji-cheng Tao
  • Ya-zhou Han
Article
  • 66 Downloads

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.

Keywords

chemotaxis model traveling wavefront weakly nonlinear analysis 

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Notes

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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Copyright information

© Editorial Committee of Applied Mathematics-A Journal of Chinese Universities and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Man-jun Ma
    • 1
  • Hui Li
    • 1
  • Mei-yan Gao
    • 2
  • Ji-cheng Tao
    • 3
  • Ya-zhou Han
    • 3
  1. 1.Department of Mathematics, School of SciencesZhejiang Sci-Tech UniversityHangzhouChina
  2. 2.Teaching and Research Section of MathematicsZhuji Ronghuai SchoolShaoxingChina
  3. 3.Department of Mathematics, College of ScienceChina Jiliang UniversityHangzhouChina

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