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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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
15 December 2025
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| In: |
Journal of differential equations
Year: 2025, Volume: 448, Pages: 1-47 |
| ISSN: | 1090-2732 |
| DOI: | 10.1016/j.jde.2025.113704 |
| Online Access: | 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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| Author Notes: | Chris Kowall, Anna Marciniak-Czochra, Finn Münnich |
| Summary: | 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. |
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| Item Description: | Online verfügbar: 20. August 2025, Artikelversion: 20. August 2025 Gesehen am 26.01.2026 |
| Physical Description: | Online Resource |
| ISSN: | 1090-2732 |
| DOI: | 10.1016/j.jde.2025.113704 |