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Lattice model for fast diffusion equation

Author

Listed:
  • Hernández, F.
  • Jara, M.
  • Valentim, F.

Abstract

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.

Suggested Citation

  • Hernández, F. & Jara, M. & Valentim, F., 2020. "Lattice model for fast diffusion equation," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 2808-2837.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:5:p:2808-2837
    DOI: 10.1016/j.spa.2019.08.004
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    References listed on IDEAS

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    1. Nagahata, Yukio, 2010. "Spectral gap for zero-range processes with jump rate g(x)=x[gamma]," Stochastic Processes and their Applications, Elsevier, vol. 120(6), pages 949-958, June.
    2. Hernández, Freddy & Jara, Milton & Valentim, Fábio Júlio, 2017. "Equilibrium fluctuations for a discrete Atlas model," Stochastic Processes and their Applications, Elsevier, vol. 127(3), pages 783-802.
    3. Feng, Shui & Iscoe, Ian & Seppäläinen, Timo, 1997. "A microscopic mechanism for the porous medium equation," Stochastic Processes and their Applications, Elsevier, vol. 66(2), pages 147-182, March.
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    Cited by:

    1. Yuhuan Lei & Zhonggen Su, 2023. "Hydrodynamic Limit for the d-Facilitated Exclusion Process," Journal of Theoretical Probability, Springer, vol. 36(1), pages 456-493, March.

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    2. Hernández, Freddy & Jara, Milton & Valentim, Fábio Júlio, 2017. "Equilibrium fluctuations for a discrete Atlas model," Stochastic Processes and their Applications, Elsevier, vol. 127(3), pages 783-802.
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