Stochastic Conservation Laws with Non-homogeneous Dirichlet Boundary Conditions
This paper is concerned with conservation laws with multiplicative noise on a bounded domain with non-homogeneous boundary condition.We first introduce a stochastic entropy solutions,which is new for stochastic conservation law.The existence of stochastic entropy solution can be obtained by using the method of vanishing viscosity.Using Young measure and Kruzhkov's semi-entropy formulations,uniqueness of entropy solution is proved.
scalar conservation lawentropy solutionsItô's formula
万方数据
维普
