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 journalArticlepeer-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 languageEnglish
Pages (from-to)86-117
Number of pages32
JournalBulletin des Sciences Mathematiques
Volume153
DOIs
StatePublished - Jul 2019
Externally publishedYes

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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