Séminaire de Probabilités commun ICJ/UMPA

Open asymmetric simple exclusion and scalar conservation law with unbounded source

by Lu Xu (Gran Sasso Science Institute)

Fokko du Cloux (Lyon 1)

Fokko du Cloux

Lyon 1

In this talk, we consider the asymmetric simple exclusion process on the 1-d lattice of size N.
The system exchanges particles with reservoirs at every sites, with rates that grow rapidly near the boundaries.
At the hyperbolic space-time scale, the time evolution of the macroscopic mass density is governed by the initial-boundary value problem of a quasilinear conservation law with a source term.
Different from the usual boundary-driven first-order PDE (Bardos, LeRoux, Nédélec, CPDE, 1979), the entropy solution is continuous in a weak sense at the boundaries due to the strong external effect.
The talk is based on a joint work with Linjie Zhao (HUST).