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A microscopic mechanism for the porous medium equation

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  • Feng, Shui
  • Iscoe, Ian
  • Seppäläinen, Timo

Abstract

The porous medium equation on a d-dimensional torus is obtained as a hydrodynamic scaling limit, with the usual diffusion scaling, of the empirical measures of a sequence of reversible Markov jump processes on approximating periodic lattices. Each process can be viewed as a randomly interacting configuration of sticks (or energies, etc.). The configuration evolves through exchanges of stick portions that occur between nearest neighbours through a zero-range pressure mechanism, with conservation of total sticklength.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:66:y:1997:i:2:p:147-182
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    Cited by:

    1. 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.
    2. Philipowski, Robert, 2007. "Interacting diffusions approximating the porous medium equation and propagation of chaos," Stochastic Processes and their Applications, Elsevier, vol. 117(4), pages 526-538, April.
    3. 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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