Probabilistic gradient approximation for a viscous scalar conservation law in space dimension d≥2
Benjamin Jourdain · Stochastics and stochastics reports · 2001
In this paper, we are interested in the solution of a viscous scalar conservation law. We remark that its first order spatial derivatives solve a system of partial differential equations presenting a nonlocal nonlinearity. We associate a nonlinear martingale problem with this system. After proving existence and uniqueness for the martingale problem, we obtain a propagation of chaos result for a system of interacting diffusion processes. We deduce that it is possible to approximate the solution of the viscous scalar conservation law thanks to the interacting diffusions