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

被引：1

作者：

Ferreira, L. C. F. ^{[1
]}

Santos, M. C. ^{[1
]}

Valencia-Guevara, J. C. ^{[2
]}

机构：

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

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

来源：

BULLETIN DES SCIENCES MATHEMATIQUES | 2019年 / 153卷

基金：

巴西圣保罗研究基金会;

关键词：

Fractional Laplacian; Gradient flow; Minimizing movement; Entropy; GRADIENT FLOW; DIFFUSION;

D O I：

10.1016/j.bulsci.2019.01.016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：86 / 117

页数：32

共 25 条

[1] Anomalous diffusion in view of Einstein's 1905 theory of Brownian motion [J].

Abe, S ;

Thurner, S .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2005, 356 (2-4) :403-407

[2]

Agueh M, 2005, ADV DIFFERENTIAL EQU, V10, P309

[3]

Ambrosio L., 2008, Gradient flows: in metric spaces and in the space of probability measures

[4]

[Anonymous], 2000, FUNCTIONS BOUNDED VA

[5] Continuity of the temperature in boundary heat control problems [J].

Athanasopoulos, I. ;

Caffarelli, L. A. .

ADVANCES IN MATHEMATICS, 2010, 224 (01) :293-315

[6]

Benamou JD, 2000, NUMER MATH, V84, P375, DOI 10.1007/s002119900117

[7] The Parabolic-Parabolic Keller-Segel System with Critical Diffusion as a Gradient Flow in Rd, d ≥ 3 [J].

Blanchet, Adrien ;

Laurencot, Philippe .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2013, 38 (04) :658-686

[8]

Buttazzo G., 1989, Pitman Res. Notes Math. Ser., V207

[9] GLOBAL-IN-TIME WEAK MEASURE SOLUTIONS AND FINITE-TIME AGGREGATION FOR NONLOCAL INTERACTION EQUATIONS [J].

Carrillo, J. A. ;

Difrancesco, M. ;

Figalli, A. ;

Laurent, T. ;

Slepcev, D. .

DUKE MATHEMATICAL JOURNAL, 2011, 156 (02) :229-271

[10] Example of a displacement convex functional of first order [J].

Carrillo, Jose A. ;

Slepcev, Dejan .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2009, 36 (04) :547-564

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