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高维非线性守恒律方程组 被引量：1

Multidimensional nonlinear systems of conservation laws
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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.
作者 陈恕行
机构地区 复旦大学数学科学学院
出处 《中国科学：数学》 CSCD 北大核心 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
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 conservation laws, free boundary value problem, shock, transonic flow, hyperbolic equation,mixed type equation
分类号 O175 [理学—基础数学]
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参考文献71

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同被引文献15

  • 1谷超豪，李大潜，陈恕行，等．数学物理方程(第二版)[M]．北京：高等教育出版社，1996．
  • 2徐芝纶.弹性力学(第二版)[M].北京:高等教育出版社,1987.289-294.
  • 3方卫华.大坝安全监控:问题,观点与方法[M].南京:河海大学出版社,2013.
  • 4Sheng D. Review of fundamental principles in modeling un- saturated soil behavior [ J]. Computers and Geotechnics, 2011,38(6) :757-776.
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  • 6Chang C S, Duncan J M. Consolidation analysis for partly saturated clay by using an elastic-plastic effective stress-strainmodel[J]. International Journal for Numerical and Analytical Methods Geomechanics, 1983,7( 1 ) : 39-55.
  • 7Huang S, Barbour S L, Fredlund D G. Development and verification of a coefficient of permeability function for a de- formable unsaturated soil[J]. Canadian Geotechnical Journal, 1998,35(3) :411-425.
  • 8Wu W, Li X, Charier R, et al. A thermo-hydro-mechanical constitutive model and its numerical modelling for unsaturat- ed soils[J]. Computers and Geotechnics, 2004,31(2) : 155- 167.
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  • 10林长好.一类二阶抛物方程解的极值原理和界[J].中山大学学报,1986,(3):50-54.

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中国科学：数学
2013年 第4期

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