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

• Autores: Pierre-Louis Lions , Juan Luis Vázquez , Panagiotis E. Souganidis
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 3, Nº 3-4, 1987, págs. 275-310
• Idioma: inglés
• DOI: 10.4171/rmi/51
• Títulos paralelos:
  • La relación entre el medio poroso y las ecuaciones eikonal en espacios de varias dimensiones.
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• Resumen

  • 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.