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, Kanako Suzuki
• E-Jahr: 2022
• Jahr: 28 August 2022
• Umfang: 23 S.
• Fussnoten: Gesehen am 07.12.2022
• Titel Quelle: Enthalten in: Journal of differential equations
• Ort Quelle: Orlando, Fla. : Elsevier, 1965
• Jahr Quelle: 2022
• Band/Heft Quelle: 337(2022), Seite 460-482
• ISSN Quelle: 1090-2732
• DOI: doi:10.1016/j.jde.2022.08.007
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: patterns
• Sach-SW: Reaction-diffusion equations
• Sach-SW: Stability
• Sach-SW: Stationary solutions
• K10plus-PPN: 1826446818

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 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]).