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) Chapter/Article |
| Language: | English |
| Published: |
28 Oct 2021
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| In: |
Arxiv
Year: 2021, Pages: 1-20 |
| DOI: | 10.48550/arXiv.2105.05023 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.48550/arXiv.2105.05023 Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/2105.05023 
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| Author Notes: | Szymon Cygan, Anna Marciniak-Czochra, Grzegorz Karch, and 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 {\it 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 {\it far-from-equilibrium} exhibiting singularities. Such discontinuous stationary solutions have been considered in our parallel work [\textit{Stable discontinuous stationary solutions to reaction-diffusion-ODE systems}, preprint (2021)]. |
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| Item Description: | Gesehen am 28.09.2022 |
| Physical Description: | Online Resource |
| DOI: | 10.48550/arXiv.2105.05023 |