Skip to main content
Log in

A short note on the persistence of ideal shock waves

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

References

  1. R.Courant and K. O.Friedrichs, Supersonic flow and shock waves. New York 1948.

  2. H. Freistühler, Rotational degeneracy of hyperbolic systems of conservation laws. Arch. Rational Mech. Anal.113, 39–64 (1991).

    Google Scholar 

  3. H. Freistühler, Dynamical stability and vanishing viscosity: a case study of a nonstrictly hyperbolic system. Comm. Pure Appl. Math.45, 561–582 (1992).

    Google Scholar 

  4. H. Freistühler, Non-uniformity of vanishing viscosity approximation. Appl. Math. Lett.6, 35–41 (1993).

    Google Scholar 

  5. H. Freistühler, On the stability of non-classical shock waves. Habilitationsschrift, RWTH Aachen, 1994.

    Google Scholar 

  6. H. Freistühler, On the persistence of ideal shock waves. Appl. Math. Lett.7, 7–11 (1994).

    Google Scholar 

  7. H. Freistühler andT.-P. Liu, Nonlinear stability of overcompressive shock waves in a rotationally invariant system of viscous conservation laws. Comm. Math. Phys.153, 147–158 (1993).

    Google Scholar 

  8. H.Freistühler and P.Szmolyan, Existence and bifurcation of viscous profiles for all intermediate magnetonydrodynamic shock waves. SIAM J. Math. Anal.26 (1995).

  9. E. Isaacson, D. Marchesin, andB. Plohr, Transitional waves for conservation laws. SIAM J. Math. Anal.21, 837–866 (1990).

    Google Scholar 

  10. A.Jeffrey and T.Taniuti, Nonlinear wave propagation. New York-London 1964.

  11. P. Lax, Hyperbolic systems of conservation laws II. Comm. Pure Appl. Math.10, 537–566 (1957).

    Google Scholar 

  12. P.Lax, Hyperbolic systems of conservation laws in several space variables. In: Current topics in p. d. e. Y. Ohya, K. Kasahara, and N. Shimakura, eds., Tokyo 1986.

  13. T.-T.Li, private communication, July 1991.

  14. T.-T.Li and W.-C.Yu, Boundary value problems for quasilinear hyperbolic systems. Duke University 1985.

  15. T.-P. Liu, The Riemann problem for general systems of conservation laws. J. Differential Equations18, 218–234 (1975).

    Google Scholar 

  16. T.-P.Liu and K.Zumbrun, Stability of an undercompressive shock. Preprint.

  17. A.Majda, Existence of multidimensional shock fronts. Amer. Math. Soc. Mem.281 (1983).

  18. A. Majda andR. Pego, Stable viscosity matrices for systems of conservation laws. J. Differential Equations56, 229–262 (1985).

    Google Scholar 

  19. D. G. Schaeffer, M. Shearer, D. Marchesin, andP. J. Paes-Leme, Solution of the Riemann problem for a prototype system of non-strictly hyperbolic conservation laws. Arch. Rational Mech. Anal.97, 299–320 (1987).

    Google Scholar 

  20. S.Schecter and M.Shearer, Riemann problems involving undercompressive shocks. In: Partial differential equations and continuum models of phase transitions, M. Rascle, D. Serre, and M. Slemrod, eds., Lecture Notes in Physics344, 187–200. Berlin-Heidelberg-New York 1989.

  21. S.Schecter and M.Shearer, Transversality for undercompressive shocks in Riemano problems. In: Viscous profiles and numerical methods for shock waves, M. Shearer, ed., Philadelphia 1991.

  22. K.Zumbrun, private communication, May 1993.

  23. K. Zumbrun, B. Plohr, andD. Marchesin, Scattering behavior of transitional shock waves. Mat. Contemp.3, 191–209 (1992).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Freistühler, H. A short note on the persistence of ideal shock waves. Arch. Math 64, 344–352 (1995). https://doi.org/10.1007/BF01198091

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01198091

Keywords

Navigation