Rigorous resonant 1-d nonlinear geometric optics
Journées équations aux dérivées partielles (1990), article no. 7, 12 p.
@article{JEDP_1990____A7_0,
     author = {Joly, Jean-Luc and M\'etivier, Guy and Rauch, Jeff},
     title = {Rigorous resonant 1-d nonlinear geometric optics},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {7},
     pages = {1--12},
     publisher = {Ecole polytechnique},
     year = {1990},
     mrnumber = {92e:35104},
     zbl = {0718.35094},
     language = {en},
     url = {http://www.numdam.org/item/JEDP_1990____A7_0/}
}
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
SP  - 1
EP  - 12
PB  - Ecole polytechnique
UR  - http://www.numdam.org/item/JEDP_1990____A7_0/
LA  - en
ID  - JEDP_1990____A7_0
ER  - 
%0 Journal Article
%A Joly, Jean-Luc
%A Métivier, Guy
%A Rauch, Jeff
%T Rigorous resonant 1-d nonlinear geometric optics
%J Journées équations aux dérivées partielles
%D 1990
%P 1-12
%I Ecole polytechnique
%U http://www.numdam.org/item/JEDP_1990____A7_0/
%G en
%F JEDP_1990____A7_0
Joly, Jean-Luc; Métivier, Guy; Rauch, Jeff. Rigorous resonant 1-d nonlinear geometric optics. Journées équations aux dérivées partielles (1990), article  no. 7, 12 p. http://www.numdam.org/item/JEDP_1990____A7_0/

[CB] Y. Choquet-Bruhat, Ondes asymptotiques et approchées pour systèmes d'equations aux dérivées partielles nonlineares, J. Math. Pure Appl. 48 (1969), 117-158. | MR | Zbl

[DM] R. Diperna and A. Majda, The validity of geometric optics for weak solutions of conservation laws, Comm. Math. Phys. 98 (1985), 313-347. | MR | Zbl

[G] O. Gues, These Rennes, January 1989, and article to appear.

[H] T. Hou, Homogenization for semilinear hyperbolic systems with oscillatory data, Comm. Pure Appl. Math 41 (1988) 471-495. | MR | Zbl

[HK] J. Hunter and J. Keller, Weakly nonlinear high frequency waves, Comm. Pure Appl. Math. 36 (1983), 547-569. | MR | Zbl

[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. | MR | Zbl

[J] J.L. Joly, Sur la propagations des oscillations semi-lineares en dimension 1 d'espace, C.R. Acad. Sc. Paris, t. 296, 1983. | MR | Zbl

[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.

[JMR2] J.L. Joly, G. Metivier, and J. Rauch, One dimensional nonlinear geometric optics, preprint. | Zbl

[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. | Numdam | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | Zbl

[JR5] J.L. Joly and J. Rauch, Justification of multidimensional single phase semilinear geometric optics, preprint. | Zbl

[MR] A. Majda and R. Rosales, Resonantly interacting weakly nonlinear hyperbolic waves I : a single space variable, Stud. Appl. Math. 71 (1984), 149-179. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[P] R. Pego, Some explicit resonating waves in weakly nonlinear gas dynamics, Studies in Applied Math 79 (1988), 263-270. | MR | Zbl

[T] L. Tartar, Solutions oscillantes des equations de Carleman, Seminaire Goulaouic-Meyer-Schwartz, 1983. | Numdam