Speed-up of traveling waves by negative chemotaxis

Quentin Griette (1) , Christopher Henderson (2) , Olga Turanova (3)

1 LMAH - Laboratoire de Mathématiques Appliquées du Havre
2 Department of Mathematics [University of Arizona]
3 Department of Mathematics [Michigan State University]

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.

Domaines: Equations aux dérivées partielles [math.AP]

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