Propagation enhancement of reaction-diffusion fronts by a line of fast diffusion

Jean-Michel Roquejoffre, University of Toulouse
Fine Hall 322

We discuss here a new model to describe biological invasions in the plane when a strong diffusion takes place on a line. By 'strong diffusion', we mean a large multiple of the Laplacian, or the fractional laplacian. The question is the asymptotic (as time goes to infinity) speed of spreading in the direction of the line and in the plane. In the case of a standard diffusion on the line, and for low diffusion, the line has no effect. Conversely, past a threshold, the line enhances the overall propagation in the plane. When the diffusion on the line is given by the fractional laplacian, this is even more dramatic: the propagation is exponential in time.