Stochastic Entropy Solutions for Stochastic Scalar Balance Laws - Jinlong Wei; Bin Liu; Rongrong Tian; Liang Ding (Entropy, 2019)
We are concerned with the initial value problem for a multidimensional balance law with multiplicative stochastic perturbations of Brownian type. Using the stochastic kinetic formulation and the Bhatnagar-Gross-Krook approximation, we prove the uniqueness and existence of stochastic entropy solutions. Furthermore, as applications, we derive the uniqueness and existence of the stochastic entropy solution for stochastic Buckley-Leverett equations and generalized stochastic Burgers type equations.