On the signed porous medium flow

Edoardo Mainini; Edoardo Mainini

doi:10.3934/nhm.2012.7.525

Networks and Heterogeneous Media

2012, Volume 7, Issue 3: 525-541. doi: 10.3934/nhm.2012.7.525

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On the signed porous medium flow

Edoardo Mainini ^{1
,}

1.
Département de Mathématiques, UMR 8628 Université Paris-Sud 11-CNRS, Bâtiment 425, Faculté des Sciences d'Orsay, Université Paris-Sud 11, F-91405 Orsay Cedex

Received: 01 December 2011 Revised: 01 July 2012
35A15, 35K55, 35K65.

We prove that the signed porous medium equation can be regarded as limit of an optimal transport variational scheme, therefore extending the classical result for positive solutions of [13] and showing that an optimal transport approach is suited even for treating signed densities.
- Porous media equation,
- gradient flow,
- optimal transport,
- changing sign-solutions,
- signed transport
Citation: Edoardo Mainini. On the signed porous medium flow[J]. Networks and Heterogeneous Media, 2012, 7(3): 525-541. doi: 10.3934/nhm.2012.7.525

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Abstract

We prove that the signed porous medium equation can be regarded as limit of an optimal transport variational scheme, therefore extending the classical result for positive solutions of [13] and showing that an optimal transport approach is suited even for treating signed densities.

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