Interface dynamics of the porous medium equation with a bistable   reaction term
  We consider a degenerate partial differential equation arising in population dynamics, namely the porous medium equation with a bistable reaction term. We study its asymptotic behavior as a small parameter, related to the thickness of a diffuse interface, tends to zero. We prove the rapid formation of transition layers which then propagate. We prove the convergence to a sharp interface limit whose normal velocity, at each point, is that of the underlying degenerate travelling wave. 
Matthieu Alfaro (I3M), Danielle Hilhorst (LM-Orsay)
math.AP