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二维标量守恒律一些新的黎曼解 被引量：2

Some new Riemann solutions for two-dimensional scalar conversation laws
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摘要 研究沿y方向非凸的标量守恒律的二维黎曼问题,初值是四片常数.应用广义特征分析方法,研究基本波及其相互作用,获得一些新的黎曼解的显式结构. The two-dimensional Riemann problem for scalar conversation laws is discussed.Here scalar conversation laws is nonconvex along the y direction,when initial data are four pieces of constants in four quadrant of the (x,y)-plane.Using the generalized characteristic analysis method,some interesting new Riemann solutions are found.
作者 余俊 杨汉春
机构地区 云南大学数学系
出处 《云南大学学报（自然科学版）》 CAS CSCD 北大核心 2005年第1期9-13,17,共6页 Journal of Yunnan University(Natural Sciences Edition)
基金 云南省自然科学基金资助项目(1999A0001Q).
关键词 守恒律 黎曼 显式结构 二维 标量 初值 常数 方向 方法 特征分析 two-dimensional scalar conversation laws generalized characteristic analysis nonconvex Riemann solutions
分类号 G01-09 [文化科学] G633.7 [文化科学—教育学]
  • 相关文献

参考文献17

  • 1余俊,杨汉春.一类n-维单个守恒律的黎曼问题(英文)[J].云南大学学报（自然科学版）,2003,25(4):296-298. 被引量：1
  • 2LINDQUIST W B. The scalar Riemann problem in two spatia dimensions: Piecewise smoothness of solutions [ J ]. SIAM J Math Anal, 1986, 17:1 178-1 197.
  • 3WAGNER D. The Riemann problem in two space dimensions for a single conservation laws[J]. SIAM J Math Anal, 1983,17: 534-559.
  • 4ZHANG T, ZHENG Y. Two-dimensional Riemann problem for a single conservation law[J]. Trans Amer Math Soc, 1989,312 : 589-619.
  • 5CHEN G Q, LI D, TAN D. Struture of Riemann solutions for 2- dimensional scalar conservation laws[J]. J Differential Equations, 1996, 127:124-147.
  • 6CHANG T, HSIAO L. Riemann problem and interaction of waves in gas dynamics[A]. BREZIS H, DOUGLAS R G, JEFFREY A, et al. Pitman monoger, Surveys in Pure and Applied Mathematics[C]. Essexi: Longrnan, 1989. 174-222.
  • 7GUCKENHEIMER J. Shocks and rarefactions in two space dimensions[J]. Arch Rational Mech Anal, 1975, 59:281-291.
  • 8ZHANG P, ZHANG T. Generalized characteristi, analysis and Guckenheimer structure [ J ]. J Differential Equations, 1999,152: 409-430.
  • 9SHENG W. Two-dimensional Riemann probler, for scalar conservation laws[J ]. J Differential Equations, 2002, 183: 239-261.
  • 10LINDQUIST W B. The scalar Riemann problem in two spatia dimensions: Piecewise smoothness of solutions[ J ]. SIAM J Math Anal, 1986, 17:1 178-1 197.?A

二级参考文献6

  • 1[1]WAGNER D W. The Riemann problem in two space dimensions for a single conservation law[J]. SIAM J Math Anal, 1983, 14: 534-559.
  • 2[2]ZHANG T, ZHENG Y. Two-dirnensional Riemann problem for a single conservation law[J]. Trans Amer Math Soc,1989, 312: 584-619.
  • 3[3]LI J, YANG S, ZHANG T. Thetwo-dimensional Riemann problem in gas dynamics[M]. Harlow UK: Longman Scientific & Technical, 2000.
  • 4[4]COURANT R, HILBERT D. Methods of mathematical physics[M]. New York: Interscience, 1962.
  • 5[5]Hanchun Yang. Generalized plane delta shock waves for n-dimensional zero-pressure gas dynamics[J]. J Mathematical Analysis and Applications, 2001, 260:18-35.
  • 6[6]ZHANG T, HSIAO L. The Riemann problem and interaction of waves in gas dynamics[M]. Essex: Longman Scientific & Technical, 1989.

同被引文献23

  • 1张同,陈贵强.SOME FUNDAMENTAL CONCEPTS ABOUT SYSTEM OF TWO SPATIAL DIMENSIONAL CONSERVATION LAWS[J]Acta Mathematica Scientia,1986(04).
  • 2John Guckenheimer.Shocks and rarefactions in two space dimensions[J]. Archive for Rational Mechanics and Analysis . 1975 (3)
  • 3Zhang P,Zhang T.Generalized characteristic analysis and Guckenheimer structure. Journal of Differential Equations . 1999
  • 4Sheng W.Two-dimensional Riemann problem for scalar conservation laws. Journal of Differential Equations . 2002
  • 5Chi-Wang Shu.Essentially Non-Oscillatory and Weighted Essentially Non-Oscill?atory Schemes for Hyper-bolic Conservation Laws. Journal of Computational Physics . 1997
  • 6Li J Q,Zhang T,Yang S L.The two-dimensional Riemann problem in gas dynamics. . 1998
  • 7G.Chen,,D.Li,and D.Tan.Structure of Riemann solutions for Z-dimensional scalar conservation laws. Journal of Differential Equations . 1996
  • 8Wagner DH.Riemann Problem in Two Space Dimensions For a Single Comervation Law. SIAM Journal on Mathematical Analysis . 1983
  • 9Lindquist W B.The scalar Riemann problem in two spatial dimensions, piecewise smoothness of solutions and its breakdown. SIAM Journal on Mathematical Analysis . 1986
  • 10Zhang T,Zheng Y X.Two-dimensional Riemann problem for a single conservation law. Transactions of the American Mathematical Society . 1989

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云南大学学报（自然科学版）
2005年 第1期

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