Scalar conservation laws with stochastic forcing
Analysis of PDEs
2014-02-25 v2 Probability
Abstract
We show that the Cauchy Problem for a randomly forced, periodic multi-dimensional scalar first-order conservation law with additive or multiplicative noise is well-posed: it admits a unique solution, characterized by a kinetic formulation of the problem, which is the limit of the solution of the stochastic parabolic approximation.
Cite
@article{arxiv.1001.5415,
title = {Scalar conservation laws with stochastic forcing},
author = {Arnaud Debussche and Julien Vovelle},
journal= {arXiv preprint arXiv:1001.5415},
year = {2014}
}