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.
Bibliographical noteFunding 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.
© 2019 Elsevier Masson SAS
- Fractional Laplacian
- Gradient flow
- Minimizing movement