Skip to main content
SpringerLink
Log in

Quasilinear geometric optics approximation

  • Conference paper
  • First Online:
Functional Analysis and Related Topics, 1991

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1540))

  • 982 Accesses

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
Price excludes VAT (USA)
  • Compact, lightweight 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. Y. Choquet-Bruhat, Ondes asymptotiques et approchées pour des systèmes d'équations aux dérivées partielles nonlinéaires, J. Math. pures et appl., 48(1969) 117–158.

    MathSciNet  MATH  Google Scholar 

  2. R. Courant and D. Hilbert, Methods of Mathematical Physics, vol. 2, Interscience Publishers, 1962, New York.

    MATH  Google Scholar 

  3. Jean-Marc Delort, Oscillations semi-linéaires multiphasées compatibles en dimension 2 ou 3 d'espace (to appear in Comm. Partial Diff. Equations).

    Google Scholar 

  4. Olivier Guès, Développement asymptotique de solutions exactes de systèmes hyperboliques quasilinéaires (to appear).

    Google Scholar 

  5. J. K. Hunter and J. B. Keller, Weakly nonlinear high frequency waves, Comm. Pure Appl. Math., 36(1983), 547–569.

    Article  MathSciNet  MATH  Google Scholar 

  6. J. K. Hunter, A. Majda and R. Rosales, Resonantly interacting, weakly nonlinear hyperbolic waves II. Several space variables, Studies in Appl. Math., 75(1986), 187–226.

    Article  MathSciNet  MATH  Google Scholar 

  7. Jean-Luc Joly and Jeffrey Rauch, Nonlinear resonance can create dense oscillations (to appear).

    Google Scholar 

  8. Jean-Luc Joly and Jeffrey Rauch, Justification of multidimensional single phase semilinear geometric optics, preprint, Univ. Bourdeaux I, 1989.

    Google Scholar 

  9. Jean-Luc Joly, Guy Métivier and Jeffrey Rauch, Remarques sur l'optique géometrique nonlinéaire multidimensionnelle, Séminaire Eq. Dérivées Partielles 1990–1991, Centre de Mathématiques, École Polytechnique, 1990.

    Google Scholar 

  10. Tosio Kato, The Cauchy problem for quasi-linear symmetric hyperbolic systems, Arch. Rat. Mech. Anal., 58(1975), 181–205.

    Article  MathSciNet  MATH  Google Scholar 

  11. Tosio Kato, Quasi-linear equations of evolution with applications to partial differential equations, Lecture Notes in Mathematics, 448(1975), 25–70, Springer-V., Berlin, etc.

    Google Scholar 

  12. S. Klainerman, Global existence for nonlinear wave equation, Comm. Pure Appl. Math., 33(1980), 43–101.

    Article  MathSciNet  MATH  Google Scholar 

  13. P. Lax, Hyperbolic systems of conservation laws and the mathematical theory of shock waves, Reg. Conf. Ser. Appl. Math., 13(1973), SIAM.

    Google Scholar 

  14. A. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, Springer-V., 1984, New York, etc.

    Book  MATH  Google Scholar 

  15. A. Majda, Nonlinear geometric optics for hyperbolic systems of conservation laws, IMA volumes in Math. and Appl., vol. 2, Oscillation Theory, Computation, and Methods of Compensated Compactness, 115–165, Springer-V., 1986.

    Google Scholar 

  16. A. Yoshikawa, Weak asymptotic solutions to hyperbolic systems of conservation laws, Lect. Notes in Num. Appl. Anal., 10(1989), 195–210.

    Google Scholar 

  17. A. Yoshikawa, Solutions containing a large parameter of a quasi-linear hyperbolic system of equations and their nonlinear geometric optics approximation, preprint.

    Google Scholar 

  18. A. Yoshikawa, Quasilinear oscillations and geometric optics, preprint.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Science Faculty of Engineering, Kyushu University, Japan

    Atsushi Yoshikawa

Authors
  1. Atsushi Yoshikawa
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Hikosaburo Komatsu

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag

About this paper

Cite this paper

Yoshikawa, A. (1993). Quasilinear geometric optics approximation. In: Komatsu, H. (eds) Functional Analysis and Related Topics, 1991. Lecture Notes in Mathematics, vol 1540. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085495

Download citation

  • DOI: https://doi.org/10.1007/BFb0085495

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56471-3

  • Online ISBN: 978-3-540-47565-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation