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Hydrodynamic limit of gradient exclusion processes with conductances | Tertuliano Franco
; Claudio Landim
; | Date: |
19 Jun 2008 | Abstract: | Fix a strictly increasing right continuous with left limits function $W: b
R o b R$ and a smooth function $Phi : [l,r] o b R$, defined on some
interval $[l,r]$ of $b R$, such that $0<b le Phi’le b^{-1}$. We prove that
the evolution, on the diffusive scale, of the empirical density of exclusion
processes, with conductances given by $W$, is described by the weak solutions
of the non-linear differential equation $partial_t
ho = (d/dx)(d/dW)
Phi(
ho)$. We derive some properties of the operator $(d/dx)(d/dW)$ and prove
uniqueness of weak solutions of the previous non-linear differential equation. | Source: | arXiv, 0806.3211 | Services: | Forum | Review | PDF | Favorites |
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