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Stability analysis and simulations of coupled bulk-surface reaction-diffusion systems

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Madzvamuse_2015_PRSA_CC_BY.pdf (919.2Kb)
Date
08/03/2015
Author
Madzvamuse, Anotida
Chung, Andy H. W.
Venkataraman, Chandrasekhar
Keywords
Bulk-surface reaction-diffusion equations
Bulk-surface finite-elements
Turing diffusively driven instability
Linear stability
Pattern formation
Robin-type boundary conditions
DAS
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Abstract
In this article, we formulate new models for coupled systems of bulk-surface reaction-diffusion equations on stationary volumes. The bulk reaction-diffusion equations are coupled to the surface reaction-diffusion equations through linear Robin-type boundary conditions. We then state and prove the necessary conditions for diffusion-driven instability for the coupled system. Owing to the nature of the coupling between bulk and surface dynamics, we are able to decouple the stability analysis of the bulk and surface dynamics. Under a suitable choice of model parameter values, the bulk reaction-diffusion system can induce patterning on the surface independent of whether the surface reaction-diffusion system produces or not, patterning. On the other hand, the surface reaction-diffusion system cannot generate patterns everywhere in the bulk in the absence of patterning from the bulk reaction-diffusion system. For this case, patterns can be induced only in regions close to the surface membrane. Various numerical experiments are presented to support our theoretical findings. Our most revealing numerical result is that, Robin-type boundary conditions seem to introduce a boundary layer coupling the bulk and surface dynamics.
Citation
Madzvamuse , A , Chung , A H W & Venkataraman , C 2015 , ' Stability analysis and simulations of coupled bulk-surface reaction-diffusion systems ' , Proceedings of the Royal Society A - Mathematical, Physical & Engineering Sciences , vol. 471 , no. 2175 , 20140546 . https://doi.org/10.1098/rspa.2014.0546
Publication
Proceedings of the Royal Society A - Mathematical, Physical & Engineering Sciences
Status
Peer reviewed
DOI
https://doi.org/10.1098/rspa.2014.0546
ISSN
1364-5021
Type
Journal article
Rights
Copyright 2015 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/ by/4.0/, which permits unrestricted use, provided the original author and source are credited.
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/8349

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