The logarithmic delay of KPP fronts in a periodic medium

Francois Hamel (1) , James Nolen (2) , Jean-Michel Roquejoffre (3) , Lenya Ryzhik (4)

1 I2M - Institut de Mathématiques de Marseille
2 Department of Mathematics [Durham]
3 IMT - Institut de Mathématiques de Toulouse UMR5219
4 Department of Mathematics [Stanford]

We consider solutions of the KPP-type equations with a periodically varying reaction rate, and compactly supported initial data. It has been shown by M. Bramson in the case of the constant reaction rate that the lag between the position of such solutions and that of the traveling waves grows as (3/2) log(t). We generalize this result to the periodic case

Domaines: Equations aux dérivées partielles [math.AP]

Francois Hamel, James Nolen, Jean-Michel Roquejoffre, Lenya Ryzhik. The logarithmic delay of KPP fronts in a periodic medium. Journal of the European Mathematical Society, 2016, 18 (3), pp.465-505. ⟨10.4171/JEMS/595⟩. ⟨hal-00815551⟩