摘要
本文关注具有非齐次Dirichlet边界条件的随机守恒律方程.首先引入了随机熵解的概念,对于随机守恒律而言,此概念对于非齐次Dirichlet边界条件的随机守恒律方程是新的.此熵解的存在性可以由粘性消去法给出.然后,利用Young测度和Kruzhkov的半熵公式,证明了随机熵解的唯一性.
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 semientropy formulations,uniqueness of entropy solution is proved.
作者
王小焕
吕广迎
石瑞艳
WANG Xiaohuan;LV Guangying;SHI Ruiyan(College of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China;School of Mathematics and Statistics,Henan University,Kaifeng 475001,China)
出处
《纯粹数学与应用数学》
2024年第1期90-105,共16页
Pure and Applied Mathematics
基金
国家自然科学基金(11901158,11771123,12171247)。
关键词
守恒定律
熵解
Itô公式
scalar conservation law
entropy solutions
Itô′s formula