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

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posted on 2023-06-08, 20:01 authored by Anotida MadzvamuseAnotida Madzvamuse, Andy H W Chung, Chandrasekhar VenkataramanChandrasekhar Venkataraman
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.

Funding

Unravelling new mathematics for 3D cell migration; G1438; LEVERHULME TRUST; RPG-2014-149

Mathematical Modelling and Analysis of Spatial Patterning on Evolving Surfaces; G0872; EPSRC-ENGINEERING & PHYSICAL SCIENCES RESEARCH COUNCIL; EP/J016780/1

History

Publication status

  • Published

File Version

  • Published version

Journal

Proceedings of the Royal Society A

ISSN

1364-5021

Publisher

The Royal Society

Issue

2175

Volume

471

Article number

a20140546

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2015-02-16

First Open Access (FOA) Date

2015-02-16

First Compliant Deposit (FCD) Date

2015-02-16

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