Derivation of the fractional porous medium equation from a microscopic dynamics

被引：0

作者：

Cardoso, Pedro ^{[1
]}

de Paula, Renato ^{[1
]}

Goncalves, Patricia ^{[1
]}

机构：

[1] Univ Lisbon, Inst Super Tecn, Ctr Math Anal Geometry & Dynam Syst, Ave Rovisco Pais 1, P-1049001 Lisbon, Portugal

来源：

NONLINEARITY | 2023年 / 36卷 / 03期

基金：

欧洲研究理事会;

关键词：

fractional porous medium equation; hydrodynamic limits; exclusion process; SYSTEM; LIMIT;

D O I：

10.1088/1361-6544/acb7c1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article we derive the fractional porous medium equation for any power of the fractional Laplacian as the hydrodynamic limit of a microscopic dynamics of random particles with long range interactions, but the jump rate highly depends on the occupancy near the sites where the interactions take place.

引用

页码：1840 / 1872

页数：33

共 50 条

[1] Microscopic Dynamics for the Porous Medium Equation
Goncalves, Patricia
DYNAMICS, GAMES AND SCIENCE II, 2011, 2 : 387 - 392
[2] Derivation of the nonlocal pressure form of the fractional porous medium equation in the hydrological setting
Plociniczak, Lukasz
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2019, 76 : 66 - 70
[3] On Microscopic Derivation of a Fractional Stochastic Burgers Equation
Sunder Sethuraman
Communications in Mathematical Physics, 2016, 341 : 625 - 665
[4] On Microscopic Derivation of a Fractional Stochastic Burgers Equation
Sethuraman, Sunder
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2016, 341 (02) : 625 - 665
[5] A fractional porous medium equation
de Pablo, Arturo
Quiros, Fernando
Rodriguez, Ana
Luis Vazquez, Juan
ADVANCES IN MATHEMATICS, 2011, 226 (02) : 1378 - 1409
[6] Analysis and mean-field derivation of a porous-medium equation with fractional diffusion
Chen, Li
Holzinger, Alexandra
Juengel, Ansgar
Zamponi, Nicola
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2022, 47 (11) : 2217 - 2269
[7] A microscopic mechanism for the porous medium equation
Feng, S
Iscoe, I
Seppalainen, T
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1997, 66 (02) : 147 - 182
[8] A General Fractional Porous Medium Equation
de Pablo, Arturo
Quiros, Fernando
Rodriguez, Ana
Luis Vazquez, Juan
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2012, 65 (09) : 1242 - 1284
[9] Analytical studies of a time-fractional porous medium equation. Derivation, approximation and applications
Plociniczak, Lukasz
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2015, 24 (1-3) : 169 - 183
[10] The mesa problem for the fractional porous medium equation
Vazquez, Juan Luis
INTERFACES AND FREE BOUNDARIES, 2015, 17 (02) : 263 - 288

← 1 2 3 4 5 →