Hydrodynamics of Porous Medium Model with slow reservoirs

Abstract

We analyze the hydrodynamic behavior of the porous medium model in a discrete space $\{0,\dots ,n\}$, where the sites $0$ and $n$ stand for reservoirs. Our strategy relies on the entropy method of Guo, Papanicolau and Varadhan. 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, but with boundary conditions which depend on the reservoirs strength's.

arXiv comment32 pages, 3 figures

References in corpus (2)

• Glassy dynamics of kinetically constrained models
• Exclusion process with slow boundary

Cited by in corpus (5)

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• The boundary driven zero-range process
• Hydrodynamical behavior for the generalized symmetric exclusion with open boundary
• Derivation of the fractional porous medium equation from a microscopic dynamics
• Energy estimates and convergence of weak solutions of the porous medium equation