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