Boundary layers and glancing blow-up in nonlinear geometric optics
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 33 (2000) no. 3, pp. 383-432.
@article{ASENS_2000_4_33_3_383_0,
     author = {Williams, Mark},
     title = {Boundary layers and glancing blow-up in nonlinear geometric optics},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {383--432},
     publisher = {Elsevier},
     volume = {Ser. 4, 33},
     number = {3},
     year = {2000},
     doi = {10.1016/s0012-9593(00)00116-6},
     mrnumber = {2001f:35392},
     zbl = {0962.35118},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/s0012-9593(00)00116-6/}
}
TY  - JOUR
AU  - Williams, Mark
TI  - Boundary layers and glancing blow-up in nonlinear geometric optics
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 2000
SP  - 383
EP  - 432
VL  - 33
IS  - 3
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/s0012-9593(00)00116-6/
DO  - 10.1016/s0012-9593(00)00116-6
LA  - en
ID  - ASENS_2000_4_33_3_383_0
ER  - 
%0 Journal Article
%A Williams, Mark
%T Boundary layers and glancing blow-up in nonlinear geometric optics
%J Annales scientifiques de l'École Normale Supérieure
%D 2000
%P 383-432
%V 33
%N 3
%I Elsevier
%U http://www.numdam.org/articles/10.1016/s0012-9593(00)00116-6/
%R 10.1016/s0012-9593(00)00116-6
%G en
%F ASENS_2000_4_33_3_383_0
Williams, Mark. Boundary layers and glancing blow-up in nonlinear geometric optics. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 33 (2000) no. 3, pp. 383-432. doi : 10.1016/s0012-9593(00)00116-6. http://www.numdam.org/articles/10.1016/s0012-9593(00)00116-6/

[1] Cassels J.W.S., An Introduction to Diophantine Approximation, Cambridge University Press, Cambridge, 1957. | MR | Zbl

[2] Chazarain J., Piriou A., Introduction to the Theory of Linear Partial Differential Equations, North Holland, Amsterdam, 1982. | MR | Zbl

[3] Donnat P., Joly J.-L., Métivier G., Rauch J., Diffractive nonlinear geometric optics I, in : Séminaire Équations aux Dérivées Partielles, XVII, École Polytechnique, 1996, pp. 1-23. | Numdam | MR | Zbl

[4] Gues O., Développements asymptotiques de solutions exactes de systèmes hyperboliques quasilinéaires, Asymp. Anal. 6 (1993) 241-270. | MR | Zbl

[5] Gues O., Problème mixte hyperbolique quasi-linéaire caractéristique, Comm. PDE 15 (1990) 595-645. | MR | Zbl

[6] Gues O., Viscous boundary layers and high frequency oscillations, in : Singularities and Oscillations, Springer, New York, 1997. | MR | Zbl

[7] Gues O., Perturbations visqueuses de problèmes mixtes hyperboliques et couches limites, Ann. Inst. Fourier 45 (1995) 973-1006. | Numdam | MR | Zbl

[8] Joly J.-L., Métivier G., Rauch J., Coherent and focusing multidimensional nonlinear geometric optics, Ann. Scien. École Norm. Sup. 28 (1995) 51-113. | Numdam | MR | Zbl

[9] Joly J.-L., Métivier G., Rauch J., Coherent nonlinear waves and the Wiener algebra, Ann. Inst. Fourier 44 (1994) 167-196. | Numdam | MR | Zbl

[10] Joly J.-L., Métivier G., Rauch J., Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillatory waves, Duke Math. J. 70 (1993) 373-404. | MR | Zbl

[11] Joly J.-L., Métivier G., Rauch J., Diffractive nonlinear geometric optics with rectification, Preprint, Univ. de Rennes, 1998. | MR

[12] Lax P., Asymptotic solutions of oscillatory initial value problems, Duke Math. J. 24 (1957) 627-645. | MR | Zbl

[13] Majda A., Compressible fluid flow and systems of conservation laws in several space variables, Applied Math. Sc., Vol. 53, Springer, Berlin, 1984. | MR | Zbl

[14] Majda A., Artola A., Nonlinear geometric optics for hyperbolic mixed problems, in : Analyse Mathématique et Applications, Gauthier-Villars, Paris, 1988. | Zbl

[15] Métivier G., Problèmes mixtes non linéaires et stabilité des chocs multidimensionnels, Sém. Bourbaki exp. 671, Astérisque 152-153 (1987) 37-53. | Numdam | MR | Zbl

[16] Sakamoto R., Hyperbolic Boundary Value Problems, Cambridge Univ. Press, Cambridge, 1978. | MR

[17] Williams M., Nonlinear geometric optics for hyperbolic boundary problems, Comm. PDE 21 (1996) 1829-1895. | MR | Zbl

[18] Williams M., Nonlinear geometric optics for multidimensional shocks I : profile equations, C. R. Acad. Sci. Paris, Serie I 325 (1997) 975-980. | MR | Zbl

[19] Williams M., Nonlinear geometric optics for multidimensional shocks II : oscillatory exact shocks, C. R. Acad. Sci. Paris, Serie I 325 (1997) 981-986. | MR | Zbl

[20] Williams M., Highly oscillatory multidimensional shocks, Comm. Pure Appl. Math. 52 (1999) 129-192. | MR | Zbl

Cité par Sources :