Stable discontinuous stationary solutions to reaction-diffusion-ODE systems
A general system of n ordinary differential equations coupled with one reaction-diffusion equation, considered in a bounded N-dimensional domain, with no-flux boundary condition is studied in a context of pattern formation. Such initial boundary value problems may have different types of stationary...
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| Main Authors: | , , , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
1 Nov 2021
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| In: |
Arxiv
Year: 2021, Pages: 1-31 |
| DOI: | 10.48550/arXiv.2111.01214 |
| Online Access: | kostenfrei kostenfrei 
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| Author Notes: | Szymon Cygan, Grzegorz Karch, Anna Marciniak-Czochra, and Kanako Suzuki |
| Summary: | A general system of n ordinary differential equations coupled with one reaction-diffusion equation, considered in a bounded N-dimensional domain, with no-flux boundary condition is studied in a context of pattern formation. Such initial boundary value problems may have different types of stationary solutions. In our parallel work [Instability of all regular stationary solutions to reaction-diffusion-ODE systems (2021)], regular (i.e. sufficiently smooth) stationary solutions are shown to exist, however, all of them are unstable. The goal of this work is to construct discontinuous stationary solutions to general reaction-diffusion-ODE systems and to find sufficient conditions for their stability. |
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| Item Description: | Artikelversion vom 13. April 2023 Gesehen am 09.01.2024 |
| Physical Description: | Online Resource |
| DOI: | 10.48550/arXiv.2111.01214 |