We study the relation between the porous medium equation , and the eikonal equation . Under quite general assumptions, we prove that the pressure and the interface of the solution of the Cauchy problem for the porous medium equation converge as 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.
Cite this article
Pierre-Louis Lions, Panagiotis E. Souganidis, Juan Luis Vázquez, The Relation Between the Porous Medium and the Eikonal Equations in Several Space Dimensions. Rev. Mat. Iberoam. 3 (1987), no. 3, pp. 275–310DOI 10.4171/RMI/51