Kavallaris2020_Article_DynamicsOfShadowSystemOfASingu.pdf (1.23 MB)
Dynamics of shadow system of a singular Gierer-Meinhardt system on an evolving domain
Version 2 2023-06-12, 09:31
Version 1 2023-06-09, 21:45
journal contribution
posted on 2023-06-12, 09:31 authored by Nikos I Kavallaris, Raquel Bareira, Anotida MadzvamuseAnotida MadzvamuseThe main purpose of the current paper is to contribute towards the comprehension of the dynamics of the shadow system of a singular Gierer–Meinhardt model on an isotropically evolving domain. In the case where the inhibitor’s response to the activator’s growth is rather weak, then the shadow system of the Gierer–Meinhardt model is reduced to a single though non-local equation whose dynamics is thoroughly investigated throughout the manuscript. The main focus is on the derivation of blow-up results for this non-local equation, which can be interpreted as instability patterns of the shadow system. In particular, a diffusion-driven instability (DDI), or Turing instability, in the neighbourhood of a constant stationary solution, which then is destabilised via diffusion-driven blow-up, is observed. The latter indicates the formation of some unstable patterns, whilst some stability results of global-in-time solutions towards non-constant steady states guarantee the occurrence of some stable patterns. Most of the theoretical results are verified numerically, whilst the numerical approach is also used to exhibit the dynamics of the shadow system when analytical methods fail.
Funding
Unravelling new mathematics for 3D cell migration; G1438; LEVERHULME TRUST; RPG-2014-149
InCeM: Research Training Network on Integrated Component Cycling in Epithelial Cell Motility; G1546; EUROPEAN UNION
New predictive mathematical and computational models in experimental sciences; G1949; ROYAL SOCIETY; WM160017
History
Publication status
- Published
File Version
- Published version
Journal
Journal of Nonlinear ScienceISSN
0938-8974Publisher
SpringerExternal DOI
Issue
1Volume
31Page range
1-34Article number
a5Pages
33.0Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2020-10-05First Open Access (FOA) Date
2021-01-18First Compliant Deposit (FCD) Date
2020-10-02Usage metrics
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