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一类n-维单个守恒律的黎曼问题(英文) 被引量：1

A riemann problem in n dimensions for a dingle conservation law
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摘要 借助于广义平面波解,解析地求解了一类n-维的单个守恒律的黎曼问题,所获得的解展示了两种不同的几何结构,包括一个中心疏散波和一个激波. With the help of generalized plane wave solution, a Riemann problem for a ndimensional single conservation law has been solved analytically.The solutions reveal two different geometric structures including a centred rarefaction wave and a shock wave.
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 2003年第4期296-298,共3页 Journal of Yunnan University(Natural Sciences Edition)
基金 SupportedbyNSFofYunnanProvince(1999A0 0 0 1Q) .
关键词 广义平面波解 守恒律 中心疏散波 激波 熵条件 n-维空间变量 n space dimensions generalized plane wave solution rarefaction wave shock wave entropy condition
分类号 O186.12 [理学—基础数学]
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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16

  • 1LINDQUIST 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.
  • 2WAGNER D. The Riemann problem in two space dimensions for a single conservation laws[J]. SIAM J Math Anal, 1983,17: 534-559.
  • 3CHANG 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.
  • 4GUCKENHEIMER J. Shocks and rarefactions in two space dimensions[J]. Arch Rational Mech Anal, 1975, 59:281-291.
  • 5ZHANG P, ZHANG T. Generalized characteristi, analysis and Guckenheimer structure [ J ]. J Differential Equations, 1999,152: 409-430.
  • 6SHENG W. Two-dimensional Riemann probler, for scalar conservation laws[J ]. J Differential Equations, 2002, 183: 239-261.
  • 7LINDQUIST 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
  • 8WAGNER D. The Riemann problem in two space dimensions for a single conservation laws[J]. SIAM J Math Anal, 1983,17: 534-559.?A
  • 9ZHANG T, ZHENG Y. Two-dimensional Riemann problem for a single conservation law[J]. Trans Amer Math Soc, 1989,312: 589-619.?A
  • 10CHEN G Q, LI D, TAN D. Struture of Riemann solutions for 2 - dimensional scalar conservation laws [ J ]. J Differential Equations, 1996, 127:124-147.?A

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云南大学学报（自然科学版）
2003年 第4期

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