Derivation of the fractional porous medium equation from a microscopic dynamics
arXiv:2205.00812 · doi:10.1088/1361-6544/acb7c1
Abstract
In this article we derive the fractional porous medium equation for any power of the fractional Laplacian as the hydrodynamic limit of a microscopic dynamics of random particles with long range interactions, but the jump rate highly depends on the occupancy near the sites where the interactions take place.
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- Hydrodynamic limit of particle systems with long jumps
- Hydrodynamics of Porous Medium Model with slow reservoirs
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- Hydrodynamic limit for a boundary driven super-diffusive symmetric exclusion
- From Exclusion to Slow and Fast Diffusion