Skip to main content
  • 1629 Accesses

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Boillat and T. Ruggeri, Hyperbolic principal subsystems: entropy convexity and subcharacteristic conditions. Arch. Rational Mech. Anal. 137 (1997), no. 4, 305–320.

    Article  MATH  MathSciNet  Google Scholar 

  2. G.Q. Chen, C.D. Levermore et T.P. Liu, Hyperbolic conservation laws with stiff relaxation and entropy, Communications in Pure an Applied Mathematics, 47 787–830, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  3. F. Berthelin et F. Bouchut, Weak solutions for a hyperbolic system with unilateral constraint and mass loss, Ann. IHP Analyse non linéaire, 20, pp 975–997, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  4. J.F. Colombeau and A.Y. Leroux, Multiplications of distributions in elasticity and hydrodynamics. J. Math. Phys. 29 (1988), no. 2, 315–319.

    Article  MATH  MathSciNet  Google Scholar 

  5. Dal Maso, Le Floch et F. Murat, Definition and weak stability of non conservative products, J. Math. Pures Appl., 74 (1995), 458–483.

    MathSciNet  Google Scholar 

  6. B. Després, Weak Rankine Hugoniot relation for conservation laws with convex primitive constraints, CRAS Paris, Serie I, 342, p 73–78, 2006.

    Google Scholar 

  7. B. Després, A geometrical approach to non conservative shocks and elastoplastic shocks, to appear in Arch. Rat. Mech. Anal.

    Google Scholar 

  8. P.D. Lax, Hyperbolic systems of conservation laws and the theory of shock waves, SIAM, Philadelphia, 1973.

    MATH  Google Scholar 

  9. P. Le Floch, Entropy weak solutions to nonlinear hyperbolic systems under non conservative form, Comm. In P.D.E., 13 (6), 669–727, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  10. I. Müller and T. Ruggeri, Rational Extended Thermodynamics, Springer, 1998.

    Google Scholar 

  11. M. Rascle, Elasto-Plasticity as a Zero-Relaxation Limit of Elastic Visco-Plasticity, Transp. Theory and Stat. Physics, 25 (3–5), 477–489, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  12. D. Serre, Systems of conservation, Cambridge University Press, I (1999) and II (2000). Diderot, France, 1996.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Després, B. (2008). The Weak Rankine Hugoniot Inequality. In: Benzoni-Gavage, S., Serre, D. (eds) Hyperbolic Problems: Theory, Numerics, Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75712-2_41

Download citation

Publish with us

Policies and ethics