一类二维守恒律方程的初边值问题  

The Initial And Boundary Value Problem of a Class of Two Dimensional Scalar Conservation Law

作　　者：阚辉 杨小舟 KAN Hu;YANG Xiaozhou(Wuhan Institute of Physics and Mathematics,Chinese Academy of Sciences,Wuhan 430071,China)

机构地区：[1]中国科学院武汉物理与数学研究所

出　　处：《应用数学学报》2019年第6期793-812,共20页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金青年基金(11801551)和面上基金(11471332)资助项目

摘　　要：本文主要研究单个非线性双曲守恒律的二维Riemann初边值问题,其中边界为二维斜光滑柱面,初值和边值均为常数,为了研究边界为直纹面的情形,首先要研究和构造其对应的初值问题的全局解和解的区域,验证得到的解满足Rankine-Hugoniot边界条件,内部摘条件不等式,再将所得到的解限制在边界范围内,验证它满足边界爛条件不等式,从而得到单个守恒律的二维Riemann初值问题的非自模的整体弱爛解.We study two-dimensional Riemann initial-boundary value problems for thescalar conservation law in this paper, where the boundary is a smooth two-dimensionalmanifold, the initial data and the boundary data are both constants. We study the twodimensionalRiemann initial-boundary value problems where the expression of boundaryis ruled surface, we first construet the corresponding global weak entropy solution of twodimensionalRiemann initial value problems for the scalar conservation law, and then verifythat the solutions satisfy Rankine-Hugoniont condition and Kruzkov entropy condition, ect.Secondly, restricted in the region with boundary, the solutions are verified to satisfy theentropy inequality for boundary condition. Thus, we get the global weak entropy solutionsof two-dimensional Riemann initial-boundary value problems for the scalar conservation law.

关 键 词：二维守恒律方程 二维黎曼问题 二维初边值问题 

分 类 号：O177.91[理学—数学]