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Hydrodynamical behavior of symmetric exclusion with slow bonds | | Tertuliano Franco
; Patricia Goncalves
; Adriana Neumann
; | | Date: |
22 Oct 2010 | | Abstract: | We consider the exclusion process in the one-dimensional discrete torus with
$N$ points, where all the bonds have conductance one, except a finite number of
slow bonds, with conductance $N^{-eta}$, with $etain[0,infty)$. We prove
that the time evolution of the empirical density of particles, in the diffusive
scaling, has a distinct behavior according to the range of the parameter
$eta$. If $etain [0,1)$, the hydrodynamic limit is given by the usual heat
equation. If $eta=1$, it is given by a parabolic equation involving an
operator $frac{d}{dx}frac{d}{dW}$, where $W$ is the Lebesgue measure on the
torus plus the sum of the Dirac measure supported on each macroscopic point
related to the slow bond. If $etain(1,infty)$, it is given by the heat
equation with Neumann’s boundary conditions, meaning no passage through the
slow bonds in the continuum. | | Source: | arXiv, 1010.4769 | | Services: | Forum | Review | PDF | Favorites | |
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