# 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

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topLions, 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 > 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 > 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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