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Hydrodynamics of Porous Medium Model with Slow Reservoirs

Abstract

We analyze the hydrodynamic behavior of the porous medium model (PMM) in a discrete space \(\{0,\ldots , n\}\), where the sites 0 and n stand for reservoirs. Our strategy relies on the entropy method of Guo et al. (Commun Math Phys 118:31–59, 1988). However, this method cannot be straightforwardly applied, since there are configurations that do not evolve according to the dynamics (blocked configurations). In order to avoid this problem, we slightly perturbed the dynamics in such a way that the macroscopic behavior of the system keeps following the porous medium equation (PME), but with boundary conditions which depend on the reservoirs’ strength.

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Acknowledgements

A.N. was supported through a Grant “L’ORÉAL - ABC - UNESCO Para Mulheres na Ciência”. R.P. thanks FCT/Portugal for support through the project Lisbon Mathematics PhD (LisMath). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovative programme (Grant Agreement No 715734).

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Correspondence to P. Gonçalves.

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Communicated by Stefano Olla.

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Bonorino, L., de Paula, R., Gonçalves, P. et al. Hydrodynamics of Porous Medium Model with Slow Reservoirs. J Stat Phys 179, 748–788 (2020). https://doi.org/10.1007/s10955-020-02550-y

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Keywords

  • Porous medium model
  • Hydrodynamic limit
  • Porous medium equation
  • Boundary conditions