Coherent and focusing multidimensional nonlinear geometric optics

J.-L. Joly; G. Métivier; J. Rauch

Annales scientifiques de l'École Normale Supérieure (1995)

  • Volume: 28, Issue: 1, page 51-113
  • ISSN: 0012-9593

How to cite

top

Joly, J.-L., Métivier, G., and Rauch, J.. "Coherent and focusing multidimensional nonlinear geometric optics." Annales scientifiques de l'École Normale Supérieure 28.1 (1995): 51-113. <http://eudml.org/doc/82378>.

@article{Joly1995,
author = {Joly, J.-L., Métivier, G., Rauch, J.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {nonlinear geometric optics; fast oscillation; eikonal equation},
language = {eng},
number = {1},
pages = {51-113},
publisher = {Elsevier},
title = {Coherent and focusing multidimensional nonlinear geometric optics},
url = {http://eudml.org/doc/82378},
volume = {28},
year = {1995},
}

TY - JOUR
AU - Joly, J.-L.
AU - Métivier, G.
AU - Rauch, J.
TI - Coherent and focusing multidimensional nonlinear geometric optics
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1995
PB - Elsevier
VL - 28
IS - 1
SP - 51
EP - 113
LA - eng
KW - nonlinear geometric optics; fast oscillation; eikonal equation
UR - http://eudml.org/doc/82378
ER -

References

top
  1. [C] C. CHEVERRY, Oscillations de faible amplitude pour les systèmes 2 × 2 de lois de conservations, preprint Rennes, 1993. Zbl0852.35093
  2. [D] J.-M. DELORT, Oscillations semi-linéaires multiphasées compatibles en dimension 2 et 3 d'espace (Comm. in Partial Diff. Equ., Vol. 16, 1991, pp. 845-872). Zbl0736.35001MR92g:35138
  3. [DPM] R. DIPERNA and A. MAJDA, The validity of geometric optics for weak solutions (Comm. in Math. Phys., Vol. 98, 1985, pp. 313-347). Zbl0582.35081MR87e:35057
  4. [G1] O. GUES, Développements asymptotiques de solutions exactes de systèmes hyperboliques quasi-linéaires (Asymptotic Analysis, Vol. 6, 1993, pp. 675-678). Zbl0780.35017MR94b:35067
  5. [G2] O. GUES, Ondes multidimensionnelles ε-statifiées et oscillations (Duke Math. J., Vol. 68, 1992, pp. 401-446). Zbl0837.35086MR94a:35011
  6. [HMR] J. HUNTER, A. MAJDA and R. ROSALES, Resonantly Interacting Weakly Nonlinear Hyperbolic Waves II : Several Space Variables (Stud. Appl. Math., Vol. 75, 1986, pp. 187-226). Zbl0657.35084MR89h:35199
  7. [JMR1] J.-L. JOLY, G. METIVIER and J. RAUCH, Resonant One Dimensional Nonlinear Geometric Optics (to appear in J. Funct. Analysis, Vol. 114, No. 1, 1993, pp. 106-231). Zbl0851.35023MR94i:35118
  8. [JMR2] J.-L. JOLY, G. METIVIER and J. RAUCH, Formal and Rigorous Nonlinear High Frequency Hyperbolic Waves, in Proceedings of Varenna Conference on Nonlinear Hyperbolic Equations and Field Theory, June 1990, M. K. MURPTY, S. SPAGNOLO eds. (Pitman Research Note in Math. Series, 1992, 121, p. 143). Zbl0824.35077
  9. [JMR3] J.-L. JOLY, G. METIVIER and J. RAUCH, Remarques sur l'optique géométrique non linéaire multidimensionnelle, in Séminaire Équations aux dérivées partielles de l'École Polytechnique 1990-1991, Exposé n° 1. Zbl0749.35055
  10. [JMR4] J.-L. JOLY, G. METIVIER and J. RAUCH, Coherent Nonlinear Waves and the Wiener Algebra (Ann. Inst. Fourier, t. 44, 1994, pp. 167-196). Zbl0791.35019MR95c:35163
  11. [JMR5] J.-L. JOLY, G. METIVIER and J. RAUCH, Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillary waves (to appear in Duke Math. J., Vol. 70, No. 2, 1993, pp. 373-404). Zbl0815.35066MR94c:35048
  12. [JMR6] J.-L. JOLY, G. METIVIER and J. RAUCH, Dense oscillations for the compressible 2-D Euler equations, in Non Linear Partial Differential Equations, Séminaire Collège de France 1992-1993, Pitmann Publ. 
  13. [JR1] J.-L. JOLY and J. RAUCH, Justification of Multidimensional Single Phase Semilinear Geometric Optics (Trans. Amer. Math. Soc., Vol. 330, 1992, pp. 599-625). Zbl0771.35010MR92f:35040
  14. [JR2] J.-L. JOLY and J. RAUCH, Nonlinear Resonance can Create Dense Oscillations, in Microlocal Analysis and Nonlinear Waves, M. BEALS, R. MELROSE and J. B. RAUCH eds. (IMA Volumes in Math. and its Application, Vol. 30, Springer-Verlag). Zbl0794.35098MR92k:35180
  15. [Ka1] L. A. KALYAKIN, Long Waves Asymptotics of Solutions of Nonlinear Systems of Equations with Dispersion (Dokl. An SSSR, Vol. 288, n° 4, 1986, and Soviet Math. Dokl., Vol. 33, n° 3, 1986, pp. 769-774). Zbl0629.35015MR87j:35073
  16. [Ka2] L. A. KALYAKIN, Asymptotic Decay of a One Dimensional Wave Packet in a Nonlinear Dispersive Medium (Math. Sbornik Translation, Vol. 60, n° 2, 1988, pp. 457-484). Zbl0699.35135MR88h:35069
  17. [Ka3] L. A. KALYAKIN, Long Waves Asymptotics. Integrable Equations as Asymptotic Limit of Nonlinear Systems (Russian Mth. Surveys, Vol. 44, n° 1, 1989, pp. 3-42). Zbl0683.35082MR90g:58131
  18. [Ke] J. KELLER, On solutions of nonlinear waves operators (Comm. Pure App. Math., Vol. 10, 1957, pp. 523-530). Zbl0090.31802MR20 #3371
  19. [L1] P. LAX, Shock Waves and Entropy, in Contribution to Nonlinear Analysis, ZARANTONELLO ed., Academic Press, NY, 1971, pp. 603-634. Zbl0268.35014MR52 #14677
  20. [L2] P. LAX, Asymptotic solutions of oscillatory initial value problems (Duke Math. J., Vol. 24, 1957, pp. 627-645). Zbl0083.31801MR20 #4096
  21. [MR] A. MAJDA and R. ROSALES, Resonantly Interacting Weakly Nonlinear Hyperbolic Waves I : a Single Space Variables Stud. Appl. Math., Vol. 71, 1984, pp. 149-179). Zbl0572.76066MR86e:35089
  22. [RR] J. RAUCH and M. REED, Striated solutions of semilinear twospeed wave equations (Indiana Univ. Math. J., Vol. 34, 1985, pp. 337-353). Zbl0559.35053MR86m:35111
  23. [S1] S. SCHOCHET, Fast singular limits of hyperbolic partial differential equations (to appear in J. Diff. Equ.). Zbl0838.35071
  24. [S2] S. SCHOCHET, Resonant nonlinear geometric optics for weak solutions of conservations laws, preprint 1992. 
  25. [ST] M. SABLÉ TOUGERON, Justification de l'optique géométrique faiblement non linéaire pour le problème mixte : cas des concentrations, preprint, 1993. 

Citations in EuDML Documents

top
  1. Steven Schochet, The mathematical theory of low Mach number flows
  2. Jean-Luc Joly, Guy Métivier, Jeff Rauch, Focusing and absorption of nonlinear oscillations
  3. Isabelle Gallagher, Perturbation antisymétrique et oscillations dans des équations paraboliques
  4. Jean-Luc Joly, Guy Métivier, Jeffrey Rauch, Optique géométrique non linéaire et équations de Maxwell-Bloch
  5. Guy Métivier, Steven Schochet, Limite incompressible des équations d’Euler non isentropiques
  6. Steven Schochet, The mathematical theory of low Mach number flows
  7. Anatoli Babin, Alex Mahalov, Basil Nicolaenko, Fast singular oscillating limits and global regularity for the 3D primitive equations of geophysics
  8. Jean-François Coulombel, Olivier Guès, Geometric optics expansions with amplification for hyperbolic boundary value problems: Linear problems
  9. Anatoli Babin, Alex Mahalov, Basil Nicolaenko, Fast Singular Oscillating Limits and Global Regularity for the 3D Primitive Equations of Geophysics
  10. P. Donnat, J.-L. Joly, G. Métivier, J. Rauch, Diffractive nonlinear geometric optics

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.