Skip to main content

Introduction

  • Chapter

Part of the book series: Applied Mathematical Sciences ((AMS,volume 118))

Abstract

In this section, we present the general form of systems of conservation laws in several space variables and we give some important examples of such systems that arise in continuum physics.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   69.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

  • Temple, B. Global solution of the Cauchy problem for a class of 2 x 2 nonstrictly hyperbolic conservation laws, Adv. Appl. Math. 3 (1982), 335–375.

    Article  MathSciNet  MATH  Google Scholar 

  • Schaeffer, D.G. and M. Shearer. The classification of 2 x 2 systems of non-strictly hyperbolic conservation laws with application to oil recovery, Comm. Pure. Appl. Math. 40 (1987), 141–178.

    Article  MathSciNet  MATH  Google Scholar 

  • Shearer, M. Loss of strict hyperbolicity of the Buckley—Leverett equations for three phase flow in a porous medium, in Numerical simulation in oil recovery, Proceedings of the IMA workshop (1986–87), The IMA Volumes in Mathematics and its applications 11, M.F. Wheeler (Ed.), Springer-Verlag, New York (1988), 263–283.

    Google Scholar 

  • Holden, H., L. Holden, and N.H. Risebro. Some qualitative properties of 2 x 2 systems of conservation laws, in Nonlinear Evolution Equations that Change Type, IMA Volumes in Mathematics and its Applications 27, B.L. Keyfitz and M. Shearer (Eds.), Springer-Verlag, New York (1991), 67–78.

    Google Scholar 

  • Tveito, A. and R. Winther. Existence uniqueness and continuous dependence for a system of hyperbolic conservation laws modeling polymer flooding, SIAM J. Math. Anal. 22 (1991), 905–933.

    Article  MathSciNet  MATH  Google Scholar 

  • Whitham, G.B. Linear and Nonlinear Waves, Pure and applied mathematics, Wiley-Interscience, New York (1974).

    Google Scholar 

  • Holden, H. and N.H. Risebro. A mathematical model of traffic flow on a network of unidirectional roads, SIAM J. Math. Anal. 26 (4) (1995), 999–1017.

    Article  MathSciNet  MATH  Google Scholar 

  • Jeffrey, A. and T. Taniuti. Non-linear wave propagation, Mathematics in Science and Engineering 9, Academic Press, New York 1964.

    Google Scholar 

  • John, F. Formation of singularities in one-dimensional nonlinear wave propagation, Comm. Pure Appl. Math. 27 (3) (1974), 377–405.

    Article  MathSciNet  MATH  Google Scholar 

  • Whitham, G.B. Linear and Nonlinear Waves, Pure and applied mathematics, Wiley-Interscience, New York (1974).

    Google Scholar 

  • Taylor, M. Partial Differential Equations, Applied Mathematical Sciences 117, Springer-Verlag, New York (1996).

    Google Scholar 

  • Jeffrey, A. Quasilinear hyperbolic systems and waves, Research Notes in Mathematics 5, Pitman, London (1976).

    Google Scholar 

  • Taniuti, T. and K. Nishihara. Nonlinear waves, Pitman Monographs and Studies in Mathematics 15, Pitman, London (1983).

    Google Scholar 

  • Tadmor, E. and T. Tassa. On the piecewise smoothness of entropy solutions to scalar conservation laws, Comm. Part. Diff. Equations 18 (910) (1993), 1631–1652.

    Article  MathSciNet  MATH  Google Scholar 

  • Friedrichs, K.O. and P.D. Lax. Systems of conservation laws with a convex extension, Proc. Nat. Acad. Sci. U.S.A. 68 (1971), 1686–1688.

    Article  MathSciNet  MATH  Google Scholar 

  • Dafermos, C.M. The entropy rate admissibility criteria for solutions of hyperbolic conservation laws, J. Diff. Equations 14 (1973), 265–298.

    Article  MathSciNet  Google Scholar 

  • Liu, T.P. The entropy condition and the admissibility of shocks, Arch. Rat. Mech. Anal. 53 (1976), 78–88.

    MATH  Google Scholar 

  • Godlewski E. and P.-A. Raviart. Hyperbolic systems of conservation laws, Mathématiques et Applications, Ellipses, Paris, 1991.

    Google Scholar 

  • Chang, C.L. and C.L. Merkle: The relation between flux vector splitting and parabolized schemes, J. Comp. Phys. 80 (1989), 344–361.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer Science+Business Media New York

About this chapter

Cite this chapter

Godlewski, E., Raviart, PA. (1996). Introduction. In: Numerical Approximation of Hyperbolic Systems of Conservation Laws. Applied Mathematical Sciences, vol 118. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0713-9_1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-0713-9_1

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6878-9

  • Online ISBN: 978-1-4612-0713-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics