高维非线性守恒律方程组  

Multidimensional nonlinear systems of conservation laws

作　　者：陈恕行[1] 

机构地区：[1]复旦大学数学科学学院,上海200433

出　　处：《中国科学：数学》2013年第4期317-332,共16页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11031001)资助项目

摘　　要：本文根据高维非线性守恒律方程组的研究历程将这一领域的研究大体分为四个阶段:局部经典解、具扇状波结构弱解、具花状波结构弱解、整体解与混合型方程.本文据此线索回顾与介绍多年来在该领域所获得的主要成果与进展,并提出今后所面临的一些未解决的重要问题及困难.In this paper, we review the history and progress of the study in the field of multidimensional nonlinear systems of conservation laws. The course of the study can be described as local classical solutions, solutions with fan-shaped wave structure, solutions with flower-shaped wave structure, global solutions and mixed type equations. According to this line, we introduce main results obtained in recent decades, and present some open problems and difficulties.

关 键 词：守恒律 自由边值问题 激波 跨音速流 双曲型方程 混合型方程 

分 类 号：O175[理学—数学]