Cross-diffusion in reaction-diffusion models: analysis, numerics and applications

Madzvamuse, Anotida, Gerisch, Alf and Barreira, Raquel (2016) Cross-diffusion in reaction-diffusion models: analysis, numerics and applications. In: Proceedings of the 19th European Conference on Mathematics for Industry. Mathematics in industry . Springer. (Accepted)

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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.

Item Type: Book Section
Keywords: Reaction-diffusion, cross-diffusion, pattern formation, cancer invasion
Schools and Departments: School of Mathematical and Physical Sciences > Physics and Astronomy
Research Centres and Groups: Mathematics Applied to Biology Research Group
Subjects: Q Science
Q Science > QA Mathematics
Q Science > QA Mathematics > QA0297 Numerical analysis
Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
Depositing User: Anotida Madzvamuse
Date Deposited: 03 Jan 2017 16:34
Last Modified: 16 Jun 2017 01:00
URI: http://sro.sussex.ac.uk/id/eprint/66016

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Project NameSussex Project NumberFunderFunder Ref
New predictive mathematical and computational models in experimental sciencesG1949Royal SocietyUnset
Coupling Geometric PDEs with PhysicsUnsetISAAC NEWTON INSTITUTE FOR MATHEMATICAL SCIENCESUnset