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dc.contributor.authorMadzvamuse, Anotida
dc.contributor.authorChung, Andy H. W.
dc.contributor.authorVenkataraman, Chandrasekhar
dc.identifier.citationMadzvamuse , 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 .
dc.identifier.otherPURE: 240445752
dc.identifier.otherPURE UUID: ea8ab2b6-f45d-481b-957c-f4e41cdb3415
dc.identifier.otherWOS: 000351177100002
dc.identifier.otherScopus: 84943391416
dc.description.abstractIn 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.
dc.relation.ispartofProceedings of the Royal Society A - Mathematical, Physical & Engineering Sciencesen
dc.rightsCopyright 2015 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License by/4.0/, which permits unrestricted use, provided the original author and source are credited.en
dc.subjectBulk-surface reaction-diffusion equationsen
dc.subjectBulk-surface finite-elementsen
dc.subjectTuring diffusively driven instabilityen
dc.subjectLinear stabilityen
dc.subjectPattern formationen
dc.subjectRobin-type boundary conditionsen
dc.titleStability analysis and simulations of coupled bulk-surface reaction-diffusion systemsen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Applied Mathematicsen
dc.description.statusPeer revieweden

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