Zoology of a Nonlocal Cross-Diffusion Model for Two Species

@article{Carrillo2018ZoologyOA,
  title={Zoology of a Nonlocal Cross-Diffusion Model for Two Species},
  author={Jos{\'e} A. Carrillo and Yanghong Huang and Markus Schmidtchen},
  journal={SIAM J. Appl. Math.},
  year={2018},
  volume={78},
  pages={1078-1104}
}
  • José A. Carrillo, Yanghong Huang, Markus Schmidtchen
  • Published in SIAM J. Appl. Math. 2018
  • Mathematics, Computer Science
  • We study a nonlocal two species cross-interaction model with cross-diffusion. We propose a positivity preserving finite volume scheme based on the numerical method introduced in [J. A. Carrillo, A. Chertock, and Y. Huang, Commun. Comput. Phys., 17 (2015), pp. 233--258] and explore this new model numerically in terms of its long-time behaviors. Using the so-gained insights, we compute analytical stationary states and travelling pulse solutions for a particular model in the case of attractive… CONTINUE READING

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