The logarithmic delay of KPP fronts in a periodic medium
  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 
Francois Hamel, James Nolen, Jean-Michel Roquejoffre, Lenya Ryzhik
math.AP