Rigorous resonant 1-d nonlinear geometric optics

Jean-Luc Joly; Guy Métivier; Jeff Rauch

Journées équations aux dérivées partielles (1990)

  • page 1-12
  • ISSN: 0752-0360

How to cite


Joly, Jean-Luc, Métivier, Guy, and Rauch, Jeff. "Rigorous resonant 1-d nonlinear geometric optics." Journées équations aux dérivées partielles (1990): 1-12. <http://eudml.org/doc/93222>.

author = {Joly, Jean-Luc, Métivier, Guy, Rauch, Jeff},
journal = {Journées équations aux dérivées partielles},
keywords = {nonlinear geometric optics},
language = {eng},
pages = {1-12},
publisher = {Ecole polytechnique},
title = {Rigorous resonant 1-d nonlinear geometric optics},
url = {http://eudml.org/doc/93222},
year = {1990},

AU - Joly, Jean-Luc
AU - Métivier, Guy
AU - Rauch, Jeff
TI - Rigorous resonant 1-d nonlinear geometric optics
JO - Journées équations aux dérivées partielles
PY - 1990
PB - Ecole polytechnique
SP - 1
EP - 12
LA - eng
KW - nonlinear geometric optics
UR - http://eudml.org/doc/93222
ER -


  1. [CB] Y. Choquet-Bruhat, Ondes asymptotiques et approchées pour systèmes d'equations aux dérivées partielles nonlineares, J. Math. Pure Appl. 48 (1969), 117-158. Zbl0177.36404MR41 #624
  2. [DM] R. Diperna and A. Majda, The validity of geometric optics for weak solutions of conservation laws, Comm. Math. Phys. 98 (1985), 313-347. Zbl0582.35081MR87e:35057
  3. [G] O. Gues, These Rennes, January 1989, and article to appear. 
  4. [H] T. Hou, Homogenization for semilinear hyperbolic systems with oscillatory data, Comm. Pure Appl. Math 41 (1988) 471-495. Zbl0632.35039MR89k:35136
  5. [HK] J. Hunter and J. Keller, Weakly nonlinear high frequency waves, Comm. Pure Appl. Math. 36 (1983), 547-569. Zbl0547.35070MR85h:35143
  6. [HMR] J. Hunter, A. Majda, and, R. Rosales, Resonantly interacting weakly nonlinear hyperbolic waves II : several space variables, Stud. Appl. Math. 75 (1986), 187-226. Zbl0657.35084MR89h:35199
  7. [J] J.L. Joly, Sur la propagations des oscillations semi-lineares en dimension 1 d'espace, C.R. Acad. Sc. Paris, t. 296, 1983. Zbl0555.35081MR84j:35112
  8. [JMR1] J.L. Joly, G. Metivier, and J. Rauch, Formal and rigorous nonlinear high frequency waves, in Proceedings of Conference on Nonlinear Hyperbolic Equations, Como 1990, Pittman Publ. 
  9. [JMR2] J.L. Joly, G. Metivier, and J. Rauch, One dimensional nonlinear geometric optics, preprint. Zbl0851.35023
  10. [JR1] J.L. Joly and J. Rauch, Ondes oscillantes semi-linéaires en 1.d, Journées Equations aux Dérivées Partielles, St. Jean de Monts, Juin 1986, Publ. de l'École Polytechnique, Palaiseau. Zbl0614.35002MR874553
  11. [JR2] J.L. Joly and J. Rauch, Ondes oscillantes semi-linéaire à hautes fréquences, in Recent Developments in Hyperbolic Equations, (L. Cattabriga, F. Colombini, M. Murthy, S. Spagnolo, eds.), Pitman Research Notes in Math., 183 (1988), 103-115. Zbl0724.35070MR90d:35173
  12. [JR3] J.L. Joly and J. Rauch, High frequency semilinear oscillations, in Wave Motion : Theory, Modeling, and Computation (A. J. Chorin and A. J. Majda, eds.), Springer-Verlag, (1987) 202-217. Zbl0703.35103MR89c:35096
  13. [JR4] J.L. Joly and J. Rauch, Nonlinear resonance can create dense oscillations, in Microlocal Analysis and Nonlinear Waves, M. Beals, R. Melrose, and J. Rauch eds., Springer-Verlag to appear. Zbl0794.35098
  14. [JR5] J.L. Joly and J. Rauch, Justification of multidimensional single phase semilinear geometric optics, preprint. Zbl0771.35010
  15. [MR] A. Majda and R. Rosales, Resonantly interacting weakly nonlinear hyperbolic waves I : a single space variable, Stud. Appl. Math. 71 (1984), 149-179. Zbl0572.76066MR86e:35089
  16. [MRS] A. Majda, R. Rosales, and, M. Schonbek, A canonical system of integro differential equations in nonlinear acoustics, Stud. Appl. Math. 79 (1988), 205-262. Zbl0669.76103MR90g:76077
  17. [MPT] D. MacLaughlin, G. Papanicolau, L. Tartar, Weak limits of semilinear Hyperbolic systems with oscillating data, Lecture Notes in Physics 230, Springer-Verlag 1985, 277-289. Zbl0588.76137MR815948
  18. [P] R. Pego, Some explicit resonating waves in weakly nonlinear gas dynamics, Studies in Applied Math 79 (1988), 263-270. Zbl0669.76104MR90g:76078
  19. [T] L. Tartar, Solutions oscillantes des equations de Carleman, Seminaire Goulaouic-Meyer-Schwartz, 1983. Zbl0481.35010

NotesEmbed ?


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.