Speed-up of traveling waves by negative chemotaxis

Quentin Griette, Christopher Henderson, Olga Turanova

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number110115
JournalJournal of Functional Analysis
Issue number10
StatePublished - Nov 15 2023


  • Fisher-KPP
  • Nonlocal
  • Traveling waves
  • Vanishing viscosity

ASJC Scopus subject areas

  • Analysis


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