Analysis and simulations of coupled bulk-surface reaction-diffusion systems on exponentially evolving volumes

Madzvamuse, A and Chung, A H (2016) Analysis and simulations of coupled bulk-surface reaction-diffusion systems on exponentially evolving volumes. Mathematical Modelling of Natural Phenomena, 11 (5). pp. 4-32. ISSN 0973-5348

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Abstract

In this article we present a system of coupled bulk-surface reaction-diffusion equations on exponentially evolving volumes. Detailed linear stability analysis of the homogeneous steady state is carried out. It turns out that due to the nature of the coupling (linear Robin-type boundary conditions) the characterisation of the dispersion relation in the absence and presence of spatial variation (i.e. diffusion), can be decomposed as a product of the dispersion relation of the bulk and surface models thereby allowing detailed analytical tractability. As a result we state and prove the conditions for diffusion-driven instability for systems of coupled bulk-surface reaction-diffusion equations. Furthermore, we plot explicit evolving parameter spaces for the case of an exponential growth. By selecting parameter values from the parameter spaces, we exhibit pattern formation in the bulk and on the surface in complete agreement with theoretical predictions.

Item Type: Article
Keywords: Coupled bulk-surface PDEs, reaction-diffusion systems, coupled bulk-surface finite element method, domain and surface evolution, evolving parameter spaces, exponential growth
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Analysis and Partial Differential Equations Research Group
Subjects: 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 12:25
Last Modified: 07 Mar 2017 14:06
URI: http://sro.sussex.ac.uk/id/eprint/65941

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