[Finitude de la vitesse de propagation dans des milieux poreux en utilisant des techniques de transport de masse]
Dans cette Note nous utilisons des techniques de transport de masse pour donner une preuve élémentaire de la finitude de la vitesse de propagation des solutions de l'équation mono-dimensionnelle des milieux poreux. Le résultat repose sur la preuve de la propriété suivante : la différence du support entre deux solutions quelconques correspondant à des données initiales à support compact différentes est une fonction, bornée en temps, d'une métrique de Monge–Kantorovitch appropriée.
In this Note we make use of mass transportation techniques to give a simple proof of the finite speed of propagation of the solution to the one-dimensional porous medium equation. The result follows by showing that the difference of support of any two solutions corresponding to different compactly supported initial data is a bounded in time function of a suitable Monge–Kantorovich related metric.
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@article{CRMATH_2004__338_10_815_0,
author = {Carrillo, Jos\'e Antonio and Gualdani, Maria Pia and Toscani, Giuseppe},
title = {Finite speed of propagation in porous media by mass transportation methods},
journal = {Comptes Rendus. Math\'ematique},
pages = {815--818},
publisher = {Elsevier},
volume = {338},
number = {10},
year = {2004},
doi = {10.1016/j.crma.2004.03.025},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.03.025/}
}
TY - JOUR AU - Carrillo, José Antonio AU - Gualdani, Maria Pia AU - Toscani, Giuseppe TI - Finite speed of propagation in porous media by mass transportation methods JO - Comptes Rendus. Mathématique PY - 2004 SP - 815 EP - 818 VL - 338 IS - 10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.03.025/ DO - 10.1016/j.crma.2004.03.025 LA - en ID - CRMATH_2004__338_10_815_0 ER -
%0 Journal Article %A Carrillo, José Antonio %A Gualdani, Maria Pia %A Toscani, Giuseppe %T Finite speed of propagation in porous media by mass transportation methods %J Comptes Rendus. Mathématique %D 2004 %P 815-818 %V 338 %N 10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.03.025/ %R 10.1016/j.crma.2004.03.025 %G en %F CRMATH_2004__338_10_815_0
Carrillo, José Antonio; Gualdani, Maria Pia; Toscani, Giuseppe. Finite speed of propagation in porous media by mass transportation methods. Comptes Rendus. Mathématique, Tome 338 (2004) no. 10, pp. 815-818. doi : 10.1016/j.crma.2004.03.025. http://www.numdam.org/articles/10.1016/j.crma.2004.03.025/
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☆ Work partially supported by EEC network # HPRN-CT-2002-00282, by the bilateral project Azioni integrate Italia–Spagna, by the DFG Project JU359/5, by the Vigoni Project CRUI-DAAD and by the Spanish DGI-MCYT/FEDER project BFM2002-01710.
