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Reaction-Diffusion-ODE Models of Pattern Formation

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Evolutionary Equations with Applications in Natural Sciences

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2126))

Abstract

This chapter is devoted to analysis of a class of reaction-diffusion type models arising from mathematical biology. We focus on mechanisms pattern formation in reaction-diffusion equations coupled to ordinary differential equations. Such systems are applied to modelling of interactions between cellular processes and diffusing signalling factors.

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Acknowledgements

A. M-C was supported by European Research Council Starting Grant No 210680 “Multiscale mathematical modelling of dynamics of structure formation in cell systems” and Emmy Noether Programme of German Research Council (DFG).

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  1. Institute of Applied Mathematics, Interdisciplinary Center of Scientific Computing (IWR), University of Heidelberg, Heidelberg, Germany

    Anna Marciniak-Czochra

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  1. Anna Marciniak-Czochra
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Correspondence to Anna Marciniak-Czochra .

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  1. School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa

    Jacek Banasiak

  2. Département de Mathématiques, UFR des Sciences et Techniques, Besançon, France

    Mustapha Mokhtar-Kharroubi

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Marciniak-Czochra, A. (2015). Reaction-Diffusion-ODE Models of Pattern Formation. In: Banasiak, J., Mokhtar-Kharroubi, M. (eds) Evolutionary Equations with Applications in Natural Sciences. Lecture Notes in Mathematics, vol 2126. Springer, Cham. https://doi.org/10.1007/978-3-319-11322-7_8

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