Instability of all regular stationary solutions to reaction-diffusion-ODE systems

• Verfasst von: Cygan, Szymon [VerfasserIn]
• Verfasst von: Marciniak-Czochra, Anna [VerfasserIn]
• Verfasst von: Karch, Grzegorz [VerfasserIn]
• Verfasst von: Suzuki, Kanako [VerfasserIn]
• Titel: Instability of all regular stationary solutions to reaction-diffusion-ODE systems
• Verf.angabe: Szymon Cygan, Anna Marciniak-Czochra, Grzegorz Karch, and Kanako Suzuki
• E-Jahr: 2021
• Jahr: 28 Oct 2021
• Umfang: 20 S.
• Fussnoten: Gesehen am 28.09.2022
• Titel Quelle: Enthalten in: De.arxiv.org
• Ort Quelle: [S.l.] : Arxiv.org, 1991
• Jahr Quelle: 2021
• Band/Heft Quelle: (2021), Artikel-ID 2105.05023, Seite 1-20
• DOI: doi:10.48550/arXiv.2105.05023
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: 35K57, 35B35, 35B36, 92C15
• Sach-SW: Mathematics - Analysis of PDEs
• K10plus-PPN: 1817336851

Abstract

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)].