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• W3126830179 abstract "We examine a general model for the Fisher-KPP (FKPP) equation with nonlocal advection. The main interpretation of this model is as describing a diffusing and logistically growing population that is also influenced by intraspecific attraction or repulsion. For a particular choice of parameters, this specializes to the Keller-Segel-Fisher equation for chemotaxis. Our interest is in the effect of chemotaxis on the speed of traveling waves. We prove that there is a threshold such that, when interactions are weaker and more localized than this, chemotaxis, despite being non-trivial, does not influence the speed of traveling waves; that is, the minimal speed traveling wave has speed 2 as in the FKPP case. On the other hand, when the interaction is repulsive, we show that the minimal traveling wave speed is arbitrarily large in a certain asymptotic regime in which the interaction strength and length scale tend to infinity. Nous considérons un modèle général pour l'équation de Fisher-KPP (FKPP) avec advection non locale. L'interprétation principale de ce modèle est la description d'une densité de population qui diffuse et dont la taille augmente de manière logistique, mais qui est aussi influencée par des forces d'attraction et de répulsion. Pour un choix particulier de paramètres, nous retrouvons l'équation de Keller-Segel-Fisher pour la chemotaxis. Nous nous intéressons plus particulièrement aux effets de la chemotaxis sur la vitesse des ondes progressives. Nous montrons qu'il existe un seuil tel que, pour des des interactions plus faibles et plus localisées que ce seuil, la chemotaxis, malgré qu'elle soit non triviale, ne change pas la vitesse. Autrement dit, la vitesse minimale est de 2, comme pour le cas de l'équation FKPP (sans chemotaxis). En revanche, lorsque l'interaction est répulsive, nous montrons que la vitesse minimale est arbitrairement grande, dans le régime asymptotique où la force et l'échelle de longueur tendent vers l'infini." @default.
• W3126830179 created "2021-02-15" @default.
• W3126830179 creator A5054480788 @default.
• W3126830179 date "2022-11-01" @default.
• W3126830179 modified "2023-10-12" @default.
• W3126830179 title "Slow and fast minimal speed traveling waves of the FKPP equation with chemotaxis" @default.
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• W3126830179 doi "https://doi.org/10.1016/j.matpur.2022.09.004" @default.
• W3126830179 hasPublicationYear "2022" @default.
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