| |  Online-Ressource |
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| Verfasst von: | Hou, Lingling [VerfasserIn]  |
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| | Kokubu, Hiroshi [VerfasserIn] |
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| | Marciniak-Czochra, Anna [VerfasserIn] |
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| | Takagi, Izumi [VerfasserIn] |
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| Titel: | Existence of traveling wave solutions to reaction-diffusion-ODE systems with hysteresis |
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| Verf.angabe: | Lingling Hou, Hiroshi Kokubu, Anna Marciniak-Czochra, Izumi Takagi |
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| E-Jahr: | 2023 |
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| Jahr: | 15 August 2023 |
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| Umfang: | 47 S. |
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| Illustrationen: | Illustrationen |
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| Fussnoten: | Online veröffentlicht am 9. Mai 2023 ; Gesehen am 30.11.2023 |
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| Titel Quelle: | Enthalten in: Journal of differential equations |
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| Ort Quelle: | Orlando, Fla. : Elsevier, 1965 |
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| Jahr Quelle: | 2023 |
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| Band/Heft Quelle: | 364(2023) vom: Aug., Seite 667-713 |
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| ISSN Quelle: | 1090-2732 |
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| Abstract: | This paper establishes the existence of traveling wave solutions to a reaction-diffusion equation coupled with a singularly perturbed first order ordinary differential equation with a small parameter ϵ>0. The system is a toy model for biological pattern formation. Traveling wave solutions correspond to heteroclinic orbits of a fast-slow system. Under some conditions, the reduced problem (with ϵ=0) has a heteroclinic orbit with jump discontinuity, while the layer problem (i.e., the fast subsystem obtained as another limit of ϵ→0) has an orbit filling the gap. We thus construct a singular orbit by piecing together these two orbits. The traveling wave solution is obtained in the neighborhood of the singular orbit. However, unlike the classical FitzHugh-Nagumo equations, the singular orbit contains a fold point where the normal hyperbolicity breaks down and the standard Fenichel theory is not applicable. To circumvent this difficulty we employ the directional blowup method for geometric desingularization around the fold point. |
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| DOI: | doi:10.1016/j.jde.2023.04.032 |
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| URL: | Bitte beachten Sie: Dies ist ein Bibliographieeintrag. Ein Volltextzugriff für Mitglieder der Universität besteht hier nur, falls für die entsprechende Zeitschrift/den entsprechenden Sammelband ein Abonnement besteht oder es sich um einen OpenAccess-Titel handelt.
Volltext: https://doi.org/10.1016/j.jde.2023.04.032 |
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| | Volltext: https://www.sciencedirect.com/science/article/pii/S0022039623003042 |
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| | DOI: https://doi.org/10.1016/j.jde.2023.04.032 |
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| Datenträger: | Online-Ressource |
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| Sprache: | eng |
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| Sach-SW: | Directional blowups |
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| | Fast-slow systems |
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| | Fold point |
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| | Normally hyperbolic invariant manifolds |
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| | Reaction-diffusion-ODE systems |
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| | Traveling wave solutions |
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| K10plus-PPN: | 1853910457 |
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| Verknüpfungen: | → Zeitschrift |
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Existence of traveling wave solutions to reaction-diffusion-ODE systems with hysteresis / Hou, Lingling [VerfasserIn]; 15 August 2023 (Online-Ressource)
