Lattice model for fast diffusion equation

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Hernandez, F.^1,2  Jara, M.³  Valentim, F.⁴ 

[1] Univ Nacl Colombia, Dept Matemat, AK 30 45-03 111321, Bogota, Colombia

[2] Univ Fed Fluminense, Inst Matemat, Rua Mario Santos Braga S-N, BR-24020140 Niteroi, RJ, Brazil

[3] IMPA, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, RJ, Brazil

[4] Univ Fed Espirito Santo, Dept Matemat, Av Fernando Ferrari 514, BR-29075910 Vitoria, ES, Brazil

关键词: Fast diffusion equation;    Zero-range;    Relative entropy method;   

DOI  :  10.1016/j.spa.2019.08.004

来源: Elsevier

【 摘 要 】

We obtain a fast diffusion equation (FDE) as scaling limit of a sequence of zero-range process with symmetric unit rate. Fast diffusion effect comes from the fact that the diffusion coefficient goes to infinity as the density goes to zero. In order to capture this fast diffusion effect from a microscopic point of view we are led to consider a proper rescaling of a model with a typically high number of particles per site. Furthermore, we obtain some results on the convergence for the method of lines for FDE. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free