The relation between the porous medium and the eikonal equations in several space dimensions.

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

Revista Matemática Iberoamericana (1987)

  • Volume: 3, Issue: 3-4, page 275-310
  • ISSN: 0213-2230

Abstract

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We study the relation between the porous medium equation ut = Δ(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.

How to cite

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Lions, Pierre-Louis, Souganidis, Panagiotis E., and Vázquez, Juan Luis. "The relation between the porous medium and the eikonal equations in several space dimensions.." Revista Matemática Iberoamericana 3.3-4 (1987): 275-310. <http://eudml.org/doc/39356>.

@article{Lions1987,
abstract = {We study the relation between the porous medium equation ut = Δ(um), m &gt; 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.},
author = {Lions, Pierre-Louis, Souganidis, Panagiotis E., Vázquez, Juan Luis},
journal = {Revista Matemática Iberoamericana},
keywords = {Problema de Cauchy; Problema de contorno; Convergencia; Soluciones; Hamilton-Jacobi equations; Cauchy problem; porous medium equation; eikonal equation; viscosity solution; interface},
language = {eng},
number = {3-4},
pages = {275-310},
title = {The relation between the porous medium and the eikonal equations in several space dimensions.},
url = {http://eudml.org/doc/39356},
volume = {3},
year = {1987},
}

TY - JOUR
AU - Lions, Pierre-Louis
AU - Souganidis, Panagiotis E.
AU - Vázquez, Juan Luis
TI - The relation between the porous medium and the eikonal equations in several space dimensions.
JO - Revista Matemática Iberoamericana
PY - 1987
VL - 3
IS - 3-4
SP - 275
EP - 310
AB - We study the relation between the porous medium equation ut = Δ(um), m &gt; 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.
LA - eng
KW - Problema de Cauchy; Problema de contorno; Convergencia; Soluciones; Hamilton-Jacobi equations; Cauchy problem; porous medium equation; eikonal equation; viscosity solution; interface
UR - http://eudml.org/doc/39356
ER -

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