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关于一个非线性几何光学中的非严格双曲守恒律系统的研究(英文) 被引量：1

On a nonstrictly hyperbolic system of conservation laws in nonlinear geometric optics
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摘要 研究了一个产生于非线性几何光学中的非严格双曲守恒律系统.该系统具有强非线性流函数项,且狄拉克激波可能同时出现在解的两个状态变量中.通过未知函数的一个变换,该系统的非线性流函数项得到弱化,从而其黎曼问题被完全解决. This paper studies a non-strictly hyperbolic system of conservation laws with strong nonlinearity on the flux-functions arising in nonlinear geometric optics,whose solutions may contain delta shock waves in two state variables.By performing a transformation of unknown variables,the system is reduced to another one with weak nonlinearity on the flux-functions.Then the Riemann problem for the later is solved completely.
作者 杨汉春 孙文华
机构地区 云南大学数学系
出处 《纯粹数学与应用数学》 CSCD 2004年第1期1-5,23,共6页 Pure and Applied Mathematics
基金 国家自然科学基金(10226032).
关键词 非严格双曲系统 狄拉克激波 广义Rankine—Hugonoit条件 熵条件 non-strictly hyperbolic system,delta-shock,generalized Rankine-Hugoniot Relation,entropy condition.
分类号 O175.27 [理学—基础数学]
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参考文献6

  • 1Lax P D. Hyperbolic systems of conservation laws and the mathematical theory of shock waves [J].SIAM ,Philadelphia, 1973.
  • 2Li Jiequan,Yang Shuli,Zhang Tong. The two-dimensional Riemann problem in gas dynamics[M]. Longman Scientic and Technical, 1998.
  • 3Yang Hanchun. Riemann problems for a class of coupled hyperbolic systems of conservation laws[J]. J Differential Equations, 1999,159 : 447 - 484.
  • 4Lax P D. Hyperbolic systems of conservation laws and the mathematical theory of shock waves[J].SIAM. ,Philadelphia, 1973.
  • 5Li Jiequan,Yang Shuli,Zhang Tong. The two-dimensional Riemann problem in gas dynamics[M]. Longman Scientic and Technical,1998.
  • 6Yang Hanchun, Riemann problems for a class of coupled hyperbolic systems of conservation laws[J]. J.Differential Equations, 1999,159: 447-484.

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同被引文献13

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  • 10Tan Dechun, Zhang Tong, Zheng Yuxi. Delta shock waves as limits of vanishing viscosity for hyperbolic systems of conversation laws [J]. J. Differential Equations, 1994, 112(1):1-32.

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纯粹数学与应用数学
2004年 第1期

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