Section: New Results
Invariant measure of scalar first-order conservation laws with stochastic forcing
In  , under an hypothesis of non-degeneracy of the flux, we study the long-time behaviour of periodic scalar first-order conservation laws with stochastic forcing in any space dimension. For sub-cubic fluxes, we show the existence of an invariant measure. Moreover for sub-quadratic fluxes we show uniqueness and ergodicity of the invariant measure. Also, since this invariant measure is supported by for some p small, we are led to generalize to the stochastic case the theory of solutions developed by Chen and Perthame in 2003.