Speed-up of traveling waves by negative chemotaxis

We consider the traveling wave speed for Fisher-KPP (FKPP) fronts under the influence of repulsive 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 establishing 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 a new explicit lower bound on the minimal traveling wave speed and provide a novel construction of traveling waves that extends the known existence range to all parameter values.24 month embargo; 28 August 2023This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu