Optimal regularity for one-dimensional porous medium flow.

Donald G. Aronson; Luis A. Caffarelli

Revista Matemática Iberoamericana (1986)

  • Volume: 2, Issue: 4, page 357-366
  • ISSN: 0213-2230

Abstract

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We give a new proof of the Lipschitz continuity with respect to t of the pressure in a one dimensional porous medium flow. As is shown by the Barenblatt solution, this is the optimal t-regularity for the pressure. Our proof is based on the existence and properties of a certain selfsimilar solution.

How to cite

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Aronson, Donald G., and Caffarelli, Luis A.. "Optimal regularity for one-dimensional porous medium flow.." Revista Matemática Iberoamericana 2.4 (1986): 357-366. <http://eudml.org/doc/39333>.

@article{Aronson1986,
abstract = {We give a new proof of the Lipschitz continuity with respect to t of the pressure in a one dimensional porous medium flow. As is shown by the Barenblatt solution, this is the optimal t-regularity for the pressure. Our proof is based on the existence and properties of a certain selfsimilar solution.},
author = {Aronson, Donald G., Caffarelli, Luis A.},
journal = {Revista Matemática Iberoamericana},
keywords = {Ecuaciones diferenciales en derivadas parciales; Aplicación lipschitziana; regularity of non-negative solutions; porous medium equation; isentropic flow of a perfect gas; Hölder continuous; Lipschitz continuity; one- dimensional porous medium flow; Barenblatt solution; existence; selfsimilar solution},
language = {eng},
number = {4},
pages = {357-366},
title = {Optimal regularity for one-dimensional porous medium flow.},
url = {http://eudml.org/doc/39333},
volume = {2},
year = {1986},
}

TY - JOUR
AU - Aronson, Donald G.
AU - Caffarelli, Luis A.
TI - Optimal regularity for one-dimensional porous medium flow.
JO - Revista Matemática Iberoamericana
PY - 1986
VL - 2
IS - 4
SP - 357
EP - 366
AB - We give a new proof of the Lipschitz continuity with respect to t of the pressure in a one dimensional porous medium flow. As is shown by the Barenblatt solution, this is the optimal t-regularity for the pressure. Our proof is based on the existence and properties of a certain selfsimilar solution.
LA - eng
KW - Ecuaciones diferenciales en derivadas parciales; Aplicación lipschitziana; regularity of non-negative solutions; porous medium equation; isentropic flow of a perfect gas; Hölder continuous; Lipschitz continuity; one- dimensional porous medium flow; Barenblatt solution; existence; selfsimilar solution
UR - http://eudml.org/doc/39333
ER -

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