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

Autor(es)

Ferreira, L. C. F. ^[1] ; Santos, M. C. ^[1] ; Valencia-Guevara, J. C. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, IMECC, Dept Matemat, BR-13083859 Campinas, SP - Brazil

^[2] Univ Catolica San Pablo, Dept Matemat & Estadist, Arequipa - Peru

• Tipo de documento: Artigo Científico
• Fonte: BULLETIN DES SCIENCES MATHEMATIQUES; v. 153, p. 86-117, JUL 2019.
• Citações Web of Science: 0

Resumo

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 Renyi entropy. We also develop a subdifferential calculus in our setting. (C) 2019 Elsevier Masson SAS. All rights reserved. (AU)

• Processo FAPESP: 16/16104-8 - EDPs e fluxos gradientes dependentes do tempo em espaços rugosos
• Beneficiário: Lucas Catão de Freitas Ferreira
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 14/23326-1 - Transporte ótimo de massa e EDPs não-locais
• Beneficiário: Matheus Correia dos Santos
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado