Finite speed of propagation in porous media by mass transportation methods

José Antonio Carrillo; Maria Pia Gualdani; Giuseppe Toscani

doi:https://doi.org/10.1016/j.crma.2004.03.025

Finite speed of propagation in porous media by mass transportation methods

José Antonio Carrillo, Maria Pia Gualdani, Giuseppe Toscani

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

32 Citations (Scopus)

Abstract

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. © 2004 Académie des sciences. Published by Elsevier SAS. All rights reserved.

Original language	English
Pages (from-to)	815-818
Journal	Comptes Rendus Mathematique
Volume	338
DOIs	https://doi.org/10.1016/j.crma.2004.03.025
Publication status	Published - 15 May 2004

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title = "Finite speed of propagation in porous media by mass transportation methods",

abstract = "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. {\textcopyright} 2004 Acad{\'e}mie des sciences. Published by Elsevier SAS. All rights reserved.",

author = "Carrillo, {Jos{\'e} Antonio} and Gualdani, {Maria Pia} and Giuseppe Toscani",

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T1 - Finite speed of propagation in porous media by mass transportation methods

AU - Carrillo, José Antonio

AU - Gualdani, Maria Pia

AU - Toscani, Giuseppe

PY - 2004/5/15

Y1 - 2004/5/15

N2 - 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. © 2004 Académie des sciences. Published by Elsevier SAS. All rights reserved.

AB - 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. © 2004 Académie des sciences. Published by Elsevier SAS. All rights reserved.

U2 - https://doi.org/10.1016/j.crma.2004.03.025

DO - https://doi.org/10.1016/j.crma.2004.03.025

M3 - Article

VL - 338

SP - 815

EP - 818

ER -

Finite speed of propagation in porous media by mass transportation methods

Abstract

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