  The goal of this paper is to prove the existence and stability of shocks for
viscous scalar conservation laws with space periodic flux, in the
multi-dimensional case. Such a result had been proved by the first author in
one space dimension, but the extension to a multi-dimensional setting makes the
existence proof non-trivial. We construct approximate solutions by restricting
the size of the domain and then passing to the limit as the size of the domain
goes to infinity. One of the key steps is a " normalization " procedure, which
ensures that the limit objects obtained by the approximation scheme are indeed
shocks. The proofs rely on elliptic PDE theory rather than ODE arguments as in
the 1d case. Once the existence of shocks is proved, their stability follows
from classical arguments based on the theory of dynamical systems.
