Optique géométrique oscillante en présence d'un grand choc

Christophe Cheverry; Monique Sablé-Tougeron

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1999)

  • Volume: 28, Issue: 1, page 41-98
  • ISSN: 0391-173X

How to cite

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Cheverry, Christophe, and Sablé-Tougeron, Monique. "Optique géométrique oscillante en présence d'un grand choc." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 28.1 (1999): 41-98. <http://eudml.org/doc/84373>.

@article{Cheverry1999,
author = {Cheverry, Christophe, Sablé-Tougeron, Monique},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {weak solutions; oscillatory perturbations; multiphase context},
language = {fre},
number = {1},
pages = {41-98},
publisher = {Scuola normale superiore},
title = {Optique géométrique oscillante en présence d'un grand choc},
url = {http://eudml.org/doc/84373},
volume = {28},
year = {1999},
}

TY - JOUR
AU - Cheverry, Christophe
AU - Sablé-Tougeron, Monique
TI - Optique géométrique oscillante en présence d'un grand choc
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1999
PB - Scuola normale superiore
VL - 28
IS - 1
SP - 41
EP - 98
LA - fre
KW - weak solutions; oscillatory perturbations; multiphase context
UR - http://eudml.org/doc/84373
ER -

References

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  1. [B] A. Bressan, "Lectures notes on systems of conservation laws", S.I.S.S.A, Trieste1994. 
  2. [C-R] P. Cehelsky - R. Rosales, Resonantly interacting weakly nonlinear hyperbolic waves in the presence of shocks: a single space variable in a homogeneous, time independant medium, Stud. Appl. Math.74 (1986), 117-138. Zbl0652.76046MR836293
  3. [Ch] C. Cheverry, Justification de l'optique géométrique non linéaire pour un système de lois de conservation, Duke Math. J.87 (1997), 213-263. Zbl0914.35078MR1443528
  4. [Co] A. Corli, Weakly nonlinear geometric optics for hyperbolic systems of conservation laws with shock waves, Asymptotic Anal.10 (1995), 117-172. Zbl0857.35081MR1324386
  5. [C-ST] A. Corli - M. Sablé-Tougeron, Perturbations of bounded variation of a strong shock wave, J. Differential Equations138 (1997), 195-228. Zbl0881.35071MR1462267
  6. [D-M] R. Di Perna - A. Majda, The validity of nonlinear geometric optics for weak solutions of conservation laws, Comm. Math. Phys.98 (1985), 313-347. Zbl0582.35081MR788777
  7. [E-S] W E. - D. Serre, Correctors for the homogenization of conservation laws with oscillatory forcing terms, Asymptotic Anal.5 (1992), 311-316. Zbl0766.35026MR1157236
  8. [G-L] J. Glimm - P.D. Lax, "Decay of solutions of systems of hyperbolic conservation laws", Memoirs of the Amer. Math. Soc. n. 101, Providence RI, 1970. Zbl0204.11304MR265767
  9. [H-M-R] J.K. Hunter - A. Majda - R. Rosales, Resonantly interacting weakly nonlinear hyperbolic waves. II. Several space variables, Stud. Appl. Math.75 (1986), 187-226. Zbl0657.35084MR867874
  10. [J-M-R1] J.L. Joly - G. Métivier - J. Rauch, Resonant one dimensional nonlinear geometric optics, J. Funct. Anal.114 (1993), 106-231. Zbl0851.35023MR1220985
  11. [J-M-R2] J.L. Joly - G. Métivier - J. Rauch, Focusing at a point and absorption of nonlinear oscillations, Trans. Amer. Math. Soc.347 (1995), 3921-3969. Zbl0857.35087MR1297533
  12. [J] S. Junca, "Optique géométrique non linéaire, chocs forts, relaxation", thèse, Université de Nice, 1995. 
  13. [K] S.N. Kruzkov, First order quasilinear equations in several independent variables, Math. USSR-Sb.10 (1970), 217-243. Zbl0215.16203
  14. [L] P.D. Lax, Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math.10 (1957), 537-566. Zbl0081.08803MR93653
  15. [M-A] A. Majda - M. Artola, Nonlinear geometric optics for hyperbolic mixed problems, In: "Analyse Mathématique et Applications, Contribution en l'honneur de J. L. Lions", Gauthier-Villars, Paris, 1988, pp. 319-356. Zbl0674.35057MR956966
  16. [M-R] A. Majda - R. Rosales, Resonantly interacting weakly nonlinear hyperbolic waves. I. A single space variable, Stud. Appl. Math.71 (1984), 149-179. Zbl0572.76066MR760229
  17. [S] S. Schochet, Resonant nonlinear geometric optics for weak solutions of conservation laws, J. Differential Equations113 (1994), 473-504. Zbl0856.35080MR1297667
  18. [T] L. Tartar, Compacité par compensation: résultats et perspectives, In: "Nonlinear Part. Diff. Eq. and their Appl. Collège de France, vol IV". Research Notes in Math. 84, Pitman, 1983. Zbl0544.47042MR716522
  19. [V] A. Volpert, The spaces BV and quasilinear aquations, Math. USSR-Sb.2 (1967), 225-267. Zbl0168.07402

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