Minimizing movement for a fractional porous medium equation in a periodic setting

L. C.F. Ferreira; M. C. Santos; Julio Cesar Valencia Guevara

doi:10.1016/j.bulsci.2019.01.016

Minimizing movement for a fractional porous medium equation in a periodic setting

L. C.F. Ferreira, M. C. Santos, Julio Cesar Valencia Guevara

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

Abstract

We consider a fractional porous medium equation that extends the classical porous medium and fractional heat equations. The flow is studied in the space of periodic probability measures endowed with a non-local transportation distance constructed in the spirit of the Benamou–Brenier formula. For initial periodic probability measures, we show the existence of absolutely continuous curves that are generalized minimizing movements associated to Rényi entropy. We also develop a subdifferential calculus in our setting.

Original language	English
Pages (from-to)	86-117
Number of pages	32
Journal	Bulletin des Sciences Mathematiques
Volume	153
DOIs	https://doi.org/10.1016/j.bulsci.2019.01.016
State	Published - Jul 2019
Externally published	Yes

Bibliographical note

Funding Information:
LCFF acknowledges the support from CNPq grant # 308024/2015-0 and FAPESP grant # 16/16104-8 , Brazil. MCS acknowledges the support from the FAPESP grant # 2014/23326-1 , Brazil. JCV-G acknowledges the support from CNPq grant # 140674/2014-4 , Brazil.

Publisher Copyright:
© 2019 Elsevier Masson SAS

Keywords

Entropy
Fractional Laplacian
Gradient flow
Minimizing movement

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10.1016/j.bulsci.2019.01.016

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AB - We consider a fractional porous medium equation that extends the classical porous medium and fractional heat equations. The flow is studied in the space of periodic probability measures endowed with a non-local transportation distance constructed in the spirit of the Benamou–Brenier formula. For initial periodic probability measures, we show the existence of absolutely continuous curves that are generalized minimizing movements associated to Rényi entropy. We also develop a subdifferential calculus in our setting.

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KW - Fractional Laplacian

KW - Gradient flow

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JO - Bulletin des Sciences Mathematiques

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ER -

Minimizing movement for a fractional porous medium equation in a periodic setting

Abstract

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Keywords

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