Cross-Diffusion in Reaction-Diffusion Models: Analysis, Numerics, and Applications

Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)

Abstract

Cross-diffusion terms are nowadays widely used in reaction-diffusion equations encountered in models from mathematical biology and in various engineering applications. In this contribution we review the basic model equations of such systems, give an overview of their mathematical analysis, with an emphasis on pattern formation and positivity preservation, and finally we present numerical simulations that highlight special features of reaction-cross-diffusion models.

Notes

Acknowledgements

AM is a Royal Society Wolfson Research Merit Award Holder generously supported by the Wolfson Foundation. All the authors (AM, RB, AG) thank the Isaac Newton Institute for Mathematical Sciences for its hospitality during the programme Coupling Geometric PDEs with Physics for Cell Morphology, Motility and Pattern Formation; EPSRC EP/K032208/1.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Anotida Madzvamuse
    • 1
  • Raquel Barreira
    • 2
  • Alf Gerisch
    • 3
  1. 1.School of Mathematical and Physical Sciences, Department of MathematicsUniversity of SussexBrightonUK
  2. 2.Polytechnic Institute of SetubalBarreiro School of TechnologyBarreiroPortugal
  3. 3.TU Darmstadt, Fachbereich MathematikAG Numerik und Wissenschaftliches RechnenDarmstadtGermany

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