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Hydrodynamic behavior of long-range symmetric exclusion with a slow barrier: diffusive regime
- Publication Year :
- 2021
-
Abstract
- In this article we analyse the hydrodynamical behavior of the symmetric exclusion process with long jumps and in the presence of a slow barrier. The jump rates for fast bonds are given by a transition probability $p(\cdot)$ which is symmetric and has finite variance, while for slow bonds the jump rates are given $p(\cdot)\alpha n^{-\beta}$ (with $\alpha>0$ and $\beta\geq 0$), and correspond to jumps from $\mathbb{Z}_{-}^{*}$ to $\mathbb N$. We prove that: if there is a fast bond from $\mathbb{Z}_{-}^{*}$ and $\mathbb N$, then the hydrodynamic limit is given by the heat equation with no boundary conditions; otherwise, it is given by the previous equation if $0\leq \beta<1$, but for $\beta\geq 1$ boundary conditions appear, namely, we get Robin (linear) boundary conditions if $\beta=1$ and Neumann boundary conditions if $\beta>1$.
- Subjects :
- Mathematics - Probability
Mathematical Physics
Mathematics - Analysis of PDEs
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2111.02868
- Document Type :
- Working Paper