Resumen de The Relation Between the Porous Medium and the Eikonal Equations in Several Space Dimensions.

Pierre-Louis Lions, Juan Luis Vázquez, Panagiotis E. Souganidis

• We study the relation between the porous medium equation ut = ?(um), m > 1, and the eikonal equation vt = |Dv|2. Under quite general assumtions, we prove that the pressure and the interface of the solution of the Cauchy problem for the porous medium equation converge as m¯1 to the viscosity solution and the interface of the Cauchy problem for the eikonal equation. We also address the same questions for the case of the Dirichlet boundary value problem.