Instability of all regular stationary solutions to reaction-diffusion-ODE systems
A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the context of pattern formation. These initial-boundary value problems may have regular (i.e. sufficiently smooth) stationary so...
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| Main Authors: | , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
28 August 2022
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| In: |
Journal of differential equations
Year: 2022, Volume: 337, Pages: 460-482 |
| ISSN: | 1090-2732 |
| DOI: | 10.1016/j.jde.2022.08.007 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.jde.2022.08.007 Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S002203962200479X 
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| Author Notes: | Szymon Cygan, Anna Marciniak-Czochra, Grzegorz Karch, Kanako Suzuki |
| Summary: | A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the context of pattern formation. These initial-boundary value problems may have regular (i.e. sufficiently smooth) stationary solutions. This class of close-to-equilibrium patterns includes stationary solutions that emerge due to the Turing instability of a spatially constant stationary solution. The main result of this work is instability of all regular patterns. It suggests that stable stationary solutions arising in models with non-diffusive components must be far-from-equilibrium exhibiting singularities. Such discontinuous stationary solutions have been considered in our parallel work (Cygan et al., 2021 [4]). |
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| Item Description: | Gesehen am 07.12.2022 |
| Physical Description: | Online Resource |
| ISSN: | 1090-2732 |
| DOI: | 10.1016/j.jde.2022.08.007 |