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Analysis and simulations of coupled bulk-surface reaction-diffusion systems on exponentially evolving volumes
journal contribution
posted on 2023-06-09, 04:26 authored by Anotida Madzvamuse, A H ChungIn 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.
Funding
Unravelling new mathematics for 3D cell migration; G1438; LEVERHULME TRUST; RPG-2014-149
New predictive mathematical and computational models in experimental sciences; G1949; Royal Society
InCeM: Research Training Network on Integrated Component Cycling in Epithelial Cell Motility; G1546; EUROPEAN UNION; 642866 - InCeM
Mathematical Modelling and Analysis of Spatial Patterning on Evolving Surfaces; G0872; EPSRC-ENGINEERING & PHYSICAL SCIENCES RESEARCH COUNCIL; EP/J016780/1
Coupling Geometric PDEs with Physics; ISAAC NEWTON INSTITUTE FOR MATHEMATICAL SCIENCES
History
Publication status
- Published
File Version
- Accepted version
Journal
Mathematical Modelling of Natural PhenomenaISSN
0973-5348Publisher
EDP SciencesExternal DOI
Issue
5Volume
11Page range
4-32Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Analysis and Partial Differential Equations Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2017-01-03First Open Access (FOA) Date
2017-01-03First Compliant Deposit (FCD) Date
2017-01-03Usage metrics
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