Compacité par compensation trilinéaire et optique géométrique non linéaire
Séminaire Goulaouic-Schwartz (1993-1994), Exposé no. 3, 12 p. 
@article{SEDP_1993-1994____A3_0,
     author = {Joly, J. L. and M\'etivier, G. and Rauch, J.},
     title = {Compacit\'e par compensation trilin\'eaire et optique g\'eom\'etrique non lin\'eaire},
     journal = {S\'eminaire Goulaouic-Schwartz},
     note = {talk:3},
     pages = {1--12},
     year = {1993-1994},
     publisher = {Ecole Polytechnique, Centre de Math\'ematiques},
     mrnumber = {1300898},
     zbl = {0925.35098},
     language = {fr},
     url = {https://www.numdam.org/item/SEDP_1993-1994____A3_0/}
}
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Joly, J. L.; Métivier, G.; Rauch, J. Compacité par compensation trilinéaire et optique géométrique non linéaire. Séminaire Goulaouic-Schwartz (1993-1994), Exposé no. 3, 12 p.. https://www.numdam.org/item/SEDP_1993-1994____A3_0/

[BB] W. Blaschke, G. Bol, Geometrie der Gewebe, Springer-Verlag, 1938. | Zbl | JFM

[CLMS] F. Coifman, P.L. Lions, Y. Meyer, S. Semmes, Compensated compactness and Hardy spaces, C.R. Ac. Sc. Paris, 309 (1991) pp 945-949, et preprint. | Zbl

[DP1] R. Di Perna, Compensated compactness and general systems of conservation laws, Trans. of the Amer. Math. Soc, 292 (1985) pp 383-420. | Zbl | MR

[DP2] R. Di Perna, Measure valued solutions of conservation laws, Arch. for Rat. Mech. Anal., 8 (1985), pp 223-270. | Zbl | MR

[DPM] R. Di Perna, A.MAJDA, Oscillations and concentration in weak solutions of the incompressible fluid equations, Comm. in Math. Physics, 108 (1987), pp 667-689. | Zbl | MR

[E] L.C. Evans Weak convergence methods for non linear partial differential equations, Regional conference series in mathematics, 74 (1990), Providence RI, AMS. | Zbl | MR

[G1] P. Gérard, Microlocal Defect measures, Comm. in Partial Diff. Equ., 16 (1991), pp 1761-1794. | Zbl | MR

[G2] P. Gérard, Mesures semi-classiques et ondes de Bloch, in Séminaire équations aux dérivées partielles 1990-91, École Polytechnique. | Zbl | MR | Numdam

[GL] P. Gérard,E. Leichtnam, Ergodic properties of eigenfunctions for the Dirichlet problem, Duke Math. J., 71 (1993), pp 559-607. | Zbl | MR

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

[HMR] J. Hunter, A. Majda, R. Rosales, Resonantly interacting weakly nonlinear hyperbolic waves II, Studies in Appl. Math, 75 (1986), pp 187-226. | Zbl | MR

[J] J.L. Joly, Sur la propagation des oscillations par un système hperbolique nonlinéaire en dimension 1, C.R.Ac. Sc. Paris, 296 (1983). | Zbl | MR

[JMR1] J.L. Joly, G. Métivier, J. Rauch, Resonant one dimensional nonlinear geometric optics, J. Func. Anal, 114 (1993) pp 106-231. | Zbl | MR

[JMR2] J.L. Joly, G. Métivier, J. Raucii, Generic rigourous asymptotic expansions for weakly nonlinear multidimensional oscillatory waves, Duke Math. J., à paraître.. | Zbl

[JMR3] J.L. Joly, G. Métivier, J. Rauch, Coherent and focusing multidimensional nonlinear geometric optics, Ann. Scient. ENS Paris, à paraître.. | Zbl | Numdam

[JMR4] J.L. Joly, G. Métivier, J. Rauch, Coherent nonlinear waves and the Wiener algebra, Ann. Inst. Fourier, à paraître. | Zbl | Numdam

[JMR5] J.L. Joly, G. Métivier, J. Raucii, Trilinear compensated compactness and non linear geometric optics, preprint 1993. | Zbl

[K] L.A. Kalyakin, Long waves asymptotics. Integrable equations as asymptotic limits of nonlinear systems, Russian Math. Surveys, 44 (1989) pp 3-42, Uspekhi Math. Nauk., 44 (1989), pp 5-34.. | Zbl | MR

[McLPT] D.W. Mc Laugiilin, G. Papanicolaou, L. Tartar, Weak limits of semilinear hyperbolic systems with oscillating data, in Macroscopic modelling of turbulent flows, Lecture notes in Physics Springer-Verlag, 230 (1985),pp 277-298.. | Zbl | MR

[MR] A. Majda, R. Rosales, Resonantly interacting weakly nonlinear hyperbolic waves I, Studies in Appl. Math., 71 (1984), pp 149-179. | Zbl | MR

[M1] F. Murat, Compacité par compensation, Ann. Scuola Sup. di Pisa, 5 (1978) pp 489-507. | Zbl | MR | Numdam

[M2] F. Murat, Compacité par compensation: condition nécessaire et suffisante de continuité faible sous une hypothèse de rang constant, Ann. Scuola Sup. di Pisa, 8 (1981) pp 69-102. | Zbl | MR | Numdam

[P] H. Poincaré Sur les surfaces de translation et les fonctions Abéliennes, Bull. Soc. Math. France, 29 (1901), 61-86. | MR | JFM | Numdam

[S] S. Schochet, Fast singular limits of hyperbolic PDEs, J.Diff. Equ., to appear. | Zbl | MR

[T1] L. Tartar, Compensated compactness and applications to partial differential equations, in research notes in mathematics, nonlinear analysis and mechanics. Heriot-Watt symposium, vol 4, Knops R.J. ed., Pitmann Press, 1979. | Zbl | MR

[T2] L. Tartar, Solutions oscillantes des équations de Carleman, in Séminaire Goulaouic- Schwartz 1980-81, École Polytechnique. | Zbl | MR | Numdam

[T3] L.TARTAR, Étude des oscillations dans les équations aux dérivées partielles non linéaires, Trends and applications of pure mathematics to mechanics, Ciarlet-Roseau ed., Lecture notes in Physics, Springer-Verlag, 195 (1984), pp 384-412. | Zbl | MR

[T4] L. Tartar, H-measures: a new approach for studying homogeneization, oscillations and concentration effects in partial differential equations, Proc. Roy. Soc. Edinburgh Sec A, 115 (1990), pp 193-230. | Zbl | MR

[Y] L.C. Young, Lectures on the calculus of variations and optimal control theory, Philadelphia-London, W.B. Saunders Co, 1969. | Zbl | MR