Skip to main content
Log in

Interaction of elementary waves of scalar conservation laws with discontinuous flux function

  • Applied Mathematics And Mechanics
  • Published:
Journal of Shanghai University (English Edition)

Abstract

In this paper, the Riemann solutions for scalar conservation laws with discontinuous flux function were constructed. The interactions of elementary waves of the conservation laws were concerned, and the numerical simulations were given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Whitham G B. Linear and Nonlinear Waves [M]. Wiley, New York, 1974.

    Google Scholar 

  2. Diehl S. A conservation law with point source and discontinuous flux function modelling continuous sedimentation[J]. SIAMJ. Appl. Math., 1996, 56(2): 388–419.

    Article  MATH  MathSciNet  Google Scholar 

  3. Gimse T, Risebro N H. Solutions of the Cauchy problem for a conservation law with discontinuous flux functions [J]. SIAMJ. Math. Anal., 1992, 23(3): 635–648.

    Article  MATH  MathSciNet  Google Scholar 

  4. Chang Tung, Hsiao Ling. The Riemann problem and interaction of waves in gas dynamics [A]. Pitman Monographs and Surveys in Pure and Applied Mathematics 41, Longman Scientific and Technical, Harlow, 1989.

    Google Scholar 

  5. Oleinik O. Discontinuous solutions of non-linear differential equations [J]. Amer. Math. Soc. Transl., 1963, 26: 95–172.

    MathSciNet  Google Scholar 

  6. Oleinik O, Kruzkov S N. Quasi-linear second order equations with several independent variables[J]. Uspehi. Mat.Nauk, 1961, 16: 115–155.

    MathSciNet  Google Scholar 

  7. Adimurthi A, Gowda G D V. Conservation law with discontinuous flux [R]. Report 14, Max-Plank-Institut fur Mathematik, Leipzig, 2000.

    Google Scholar 

  8. Diehl S. Conservation laws with applications to continuous sedimentation[D]. Doctoral Dissertation, Lund University, 1995.

  9. Diehl S. On scalar conservation laws with point source and discontinuous flux functions [J]. SLAM J. Math. Anal., 1995, 26(6): 1425–1451.

    Article  MATH  MathSciNet  Google Scholar 

  10. Klingenberg C, Risebro N H. Convex conservation laws with discontinuous coeffients. Existence, uniqueness and asymptotic behavior[J]. Comm. PDE., 1995, 20(11–12): 1959–1990.

    Article  MATH  MathSciNet  Google Scholar 

  11. Sheng Wan-cheng. Two-dimensional Riemann problem with discontinuous flux functions for sealer conservation laws, preprint.

  12. Li J, Zhang T, Yang S. The two-dimensional Riemann problem in gas dynamics [A]. Pitman Monographs and Surveys in Pure and Applied Mathematics 98, Longman Scientific and Technical, Harlow, 1998.

    Google Scholar 

  13. Sheng W C. Two-dimensional Riemann problems for conservation laws [J]. J. Differential Equations, 2002, 183 (1): 239–261.

    Article  MATH  MathSciNet  Google Scholar 

  14. Zhang P, Zhang T. Generalized characteristic analysis and Guckenheimer structure[J]. J. Differential Equations, 1999, 152(2): 409–430.

    Article  MATH  MathSciNet  Google Scholar 

  15. Gimes T, Risebro N H. Riemann problem with a discontinuous flux fuction[A]. Third International Conference on Hyperbolic Problem, Theory, Numerical Methods and Applications [C]. Engquist B, Gustafson B, eds., Stuctenlitteratur, Lund, 1991.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Project supported by National Natural Science Foundation of China(Grant No. 10271072)

About this article

Cite this article

Wang, Gd., Sheng, Wc. Interaction of elementary waves of scalar conservation laws with discontinuous flux function. J. of Shanghai Univ. 10, 381–387 (2006). https://doi.org/10.1007/s11741-006-0077-7

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11741-006-0077-7

Key words

2000 Mathematics Subject Classification

Navigation