The shape of expansion induced by a line with fast diffusion in   Fisher-KPP equations
  We establish a new property of Fisher-KPP type propagation in a plane, in the presence of a line with fast diffusion. We prove that the line enhances the asymptotic speed of propagation in a cone of directions. Past the critical angle given by this cone, the asymptotic speed of propagation coincides with the classical Fisher-KPP invasion speed. Several qualitative properties are further derived, such as the limiting behaviour when the diffusion on the line goes to infinity. 
Henri Berestycki, Jean-Michel Roquejoffre and Luca Rossi
math.AP