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

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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>.

@article{Joly1990,
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},
}

TY - JOUR
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 -

References

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  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

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