Invariant measure of scalar first-order conservation laws with stochastic forcing
Analysis of PDEs
2013-10-15 v1
Abstract
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 Lp for some p small, we are led to generalize to the stochastic case the theory of L1 solutions developed by Chen and Perthame in 2003.
Keywords
Cite
@article{arxiv.1310.3779,
title = {Invariant measure of scalar first-order conservation laws with stochastic forcing},
author = {Arnaud Debussche and Julien Vovelle},
journal= {arXiv preprint arXiv:1310.3779},
year = {2013}
}