Nonlinear stability results for stationary solutions of reaction-diffusion-ODE systems
Reaction-diffusion-ODE systems are emerging in modeling of biological pattern formation based on the coupling of diffusive and non-diffusive spatially heterogeneous processes. They may exhibit patterns with singularities such as jump-discontinuities. This work provides nonlinear stability and instab...
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| Hauptverfasser: | , , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
15 December 2025
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| In: |
Journal of differential equations
Year: 2025, Jahrgang: 448, Pages: 1-47 |
| ISSN: | 1090-2732 |
| DOI: | 10.1016/j.jde.2025.113704 |
| Online-Zugang: | Verlag, kostenfrei, Volltext: https://doi.org/10.1016/j.jde.2025.113704 Verlag, kostenfrei, Volltext: https://www.sciencedirect.com/science/article/pii/S0022039625007314 
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| Verfasserangaben: | Chris Kowall, Anna Marciniak-Czochra, Finn Münnich |
MARC
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| 520 | |a Reaction-diffusion-ODE systems are emerging in modeling of biological pattern formation based on the coupling of diffusive and non-diffusive spatially heterogeneous processes. They may exhibit patterns with singularities such as jump-discontinuities. This work provides nonlinear stability and instability conditions for bounded stationary solutions of reaction-diffusion-ODE systems consisting of m ODEs coupled with k reaction-diffusion equations. We characterize the spectrum of the linearized operator and relate its spectral properties to the corresponding semigroup properties. Considering the function spaces L∞(Ω)m+k,L∞(Ω)m×C(Ω‾)k and C(Ω‾)m+k, we establish a sign condition on the spectral bound of the linearized operator, which implies nonlinear stability or instability of the stationary pattern. | ||
| 650 | 4 | |a Asymptotic behavior | |
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| 650 | 4 | |a Reaction-diffusion equation | |
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