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Preprints, Working Papers, ... Year : 2022

Speed-up of traveling waves by negative chemotaxis

Abstract

We consider the traveling wave speed for Fisher-KPP (FKPP) fronts under the influence of chemotaxis and provide an almost complete picture of its asymptotic dependence on parameters representing the strength and length-scale of chemotaxis. Our study is based on the convergence to the porous medium FKPP traveling wave and a hyperbolic FKPP-Keller-Segel traveling wave in certain asymptotic regimes. In this way, it clarifies the relationship between three equations that have each garnered intense interest on their own. Our proofs involve a variety of techniques ranging from entropy methods and decay of oscillations estimates to a general description of the qualitative behavior to the hyperbolic FKPP-Keller-Segel equation. For this latter equation, we, as a part of our limiting arguments, establish an explicit lower bound on the minimal traveling wave speed and provide a new construction of traveling waves that extends the known existence range to all parameter values.
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Dates and versions

hal-03820257 , version 1 (18-10-2022)
hal-03820257 , version 2 (22-11-2022)

Identifiers

  • HAL Id : hal-03820257 , version 2

Cite

Quentin Griette, Christopher Henderson, Olga Turanova. Speed-up of traveling waves by negative chemotaxis. 2022. ⟨hal-03820257v2⟩
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