Boundary layers and glancing blow-up in nonlinear geometric optics

Mark Williams

Annales scientifiques de l'École Normale Supérieure (2000)

  • Volume: 33, Issue: 3, page 383-432
  • ISSN: 0012-9593

How to cite

top

Williams, Mark. "Boundary layers and glancing blow-up in nonlinear geometric optics." Annales scientifiques de l'École Normale Supérieure 33.3 (2000): 383-432. <http://eudml.org/doc/82521>.

@article{Williams2000,
author = {Williams, Mark},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {first-order semilinear hyperbolic boundary value problems; Kreiss well-posed boundary problem; geometric optics expansion},
language = {eng},
number = {3},
pages = {383-432},
publisher = {Elsevier},
title = {Boundary layers and glancing blow-up in nonlinear geometric optics},
url = {http://eudml.org/doc/82521},
volume = {33},
year = {2000},
}

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
PB - Elsevier
VL - 33
IS - 3
SP - 383
EP - 432
LA - eng
KW - first-order semilinear hyperbolic boundary value problems; Kreiss well-posed boundary problem; geometric optics expansion
UR - http://eudml.org/doc/82521
ER -

References

top
  1. [1] CASSELS J.W.S., An Introduction to Diophantine Approximation, Cambridge University Press, Cambridge, 1957. Zbl0077.04801MR19,396h
  2. [2] CHAZARAIN J., PIRIOU A., Introduction to the Theory of Linear Partial Differential Equations, North Holland, Amsterdam, 1982. Zbl0487.35002MR83j:35001
  3. [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. Zbl0910.35076MR99m:35147
  4. [4] GUES O., Développements asymptotiques de solutions exactes de systèmes hyperboliques quasilinéaires, Asymp. Anal. 6 (1993) 241-270. Zbl0780.35017MR94b:35067
  5. [5] GUES O., Problème mixte hyperbolique quasi-linéaire caractéristique, Comm. PDE 15 (1990) 595-645. Zbl0712.35061MR91i:35122
  6. [6] GUES O., Viscous boundary layers and high frequency oscillations, in : Singularities and Oscillations, Springer, New York, 1997. Zbl0877.35072MR98j:35025
  7. [7] GUES O., Perturbations visqueuses de problèmes mixtes hyperboliques et couches limites, Ann. Inst. Fourier 45 (1995) 973-1006. Zbl0831.34023MR97i:35103
  8. [8] JOLY J.-L., MÉTIVIER G., RAUCH J., Coherent and focusing multidimensional nonlinear geometric optics, Ann. Scien. École Norm. Sup. 28 (1995) 51-113. Zbl0836.35087MR95k:35035
  9. [9] JOLY J.-L., MÉTIVIER G., RAUCH J., Coherent nonlinear waves and the Wiener algebra, Ann. Inst. Fourier 44 (1994) 167-196. Zbl0791.35019MR95c:35163
  10. [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. Zbl0815.35066MR94c:35048
  11. [11] JOLY J.-L., MÉTIVIER G., RAUCH J., Diffractive nonlinear geometric optics with rectification, Preprint, Univ. de Rennes, 1998. Zbl0928.35093MR2000d:35130
  12. [12] LAX P., Asymptotic solutions of oscillatory initial value problems, Duke Math. J. 24 (1957) 627-645. Zbl0083.31801MR20 #4096
  13. [13] MAJDA A., Compressible fluid flow and systems of conservation laws in several space variables, Applied Math. Sc., Vol. 53, Springer, Berlin, 1984. Zbl0537.76001MR85e:35077
  14. [14] MAJDA A., ARTOLA A., Nonlinear geometric optics for hyperbolic mixed problems, in : Analyse Mathématique et Applications, Gauthier-Villars, Paris, 1988. Zbl0674.35057
  15. [15] MÉTIVIER G., Problèmes mixtes non linéaires et stabilité des chocs multidimensionnels, Sém. Bourbaki exp. 671, Astérisque 152-153 (1987) 37-53. Zbl0659.35063MR89f:35131
  16. [16] SAKAMOTO R., Hyperbolic Boundary Value Problems, Cambridge Univ. Press, Cambridge, 1978. Zbl0494.35001MR82i:35101
  17. [17] WILLIAMS M., Nonlinear geometric optics for hyperbolic boundary problems, Comm. PDE 21 (1996) 1829-1895. Zbl0881.35068MR98d:35136
  18. [18] WILLIAMS M., Nonlinear geometric optics for multidimensional shocks I : profile equations, C. R. Acad. Sci. Paris, Serie I 325 (1997) 975-980. Zbl0891.35094MR98j:35122a
  19. [19] WILLIAMS M., Nonlinear geometric optics for multidimensional shocks II : oscillatory exact shocks, C. R. Acad. Sci. Paris, Serie I 325 (1997) 981-986. Zbl0891.35095MR98j:35122b
  20. [20] WILLIAMS M., Highly oscillatory multidimensional shocks, Comm. Pure Appl. Math. 52 (1999) 129-192. Zbl0929.35090MR99k:35120

NotesEmbed ?

top

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.