Global existence for the nonlinear equations of crystal optics

Otto Liess

Journées équations aux dérivées partielles (1989)

  • page 1-11
  • ISSN: 0752-0360

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Liess, Otto. "Global existence for the nonlinear equations of crystal optics." Journées équations aux dérivées partielles (1989): 1-11. <http://eudml.org/doc/93200>.

@article{Liess1989,
author = {Liess, Otto},
journal = {Journées équations aux dérivées partielles},
keywords = {Global existence; smooth solutions; dielectric tensor},
language = {eng},
pages = {1-11},
publisher = {Ecole polytechnique},
title = {Global existence for the nonlinear equations of crystal optics},
url = {http://eudml.org/doc/93200},
year = {1989},
}

TY - JOUR
AU - Liess, Otto
TI - Global existence for the nonlinear equations of crystal optics
JO - Journées équations aux dérivées partielles
PY - 1989
PB - Ecole polytechnique
SP - 1
EP - 11
LA - eng
KW - Global existence; smooth solutions; dielectric tensor
UR - http://eudml.org/doc/93200
ER -

References

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  1. J.M. Bony [1] : Calcul symbolic et propagation des singularités pour les équations aux derivées partielles non linéaires. Ann. Sc. E.N.S. 14 (1981), 209-246. Zbl0495.35024MR84h:35177
  2. M. Born - E. Wolf [1] : Principles of optics, 3rd ed., Pergamon Press, 1964. 
  3. R. Courant - D. Hilbert [1] : Methoden der mathematischen Physik. vol. II, Springer Verlag, 1937, and revised English version in Interscience Publ., 1962. Zbl0017.39702JFM63.0449.05
  4. F. John [1] : Delayed singularity formation in solutions of nonllinear wave equations in higher dimension. Comm. Pure Appl. Math., 29 (1976), 649-681. Zbl0332.35044MR55 #8570
  5. F. John [2] : Lower bounds for the life span of solutions of nonlinear wave equations in three dimensions. Comm. Pure Appl. Math., 36 (1983), 1-35. Zbl0487.35065MR84a:35172
  6. F. John [3] : Almost global existence of elastic waves of finite amplitude arising from small initial disturbances. Comm. Pure Appl. Math., 41:3 (1988), 615-667. Zbl0635.35066MR89j:35087
  7. T. Kato [1] : The Cauchy problem for quasi-linear symmetric hyperbolic systems. Arch. Rat. Mech. Anal. 58 (1975), 181-205. Zbl0343.35056MR52 #11341
  8. S. Klainerman [1] : Global existence for nonlinear wave equations. Comm. Pure Appl. Math. 33 (1980), 43-101. Zbl0405.35056MR81b:35050
  9. S. Klainerman [2] : Long time behaviour of solutions to nonlinear wave equations. Proc. Int. Congress Math. at Warsaw 1983. 1209-1215. Zbl0581.35052MR804771
  10. S. Klainerman-G. Ponce [1] : Global small amplitude solutions to nonlinear evolution equations. Comm. Pure Appl. Math., 36, (1983), 133-141. Zbl0509.35009MR84a:35173
  11. O. Liess [1] : Decay estimates for solutions of the system of crystal optics. To appear. Zbl0735.35018
  12. I.E. Segal [1] : Dispersion for nonlinear relativistic equations. Ann. E.N.S., 4e serie (1968), 459-497. Zbl0179.42302MR39 #5109
  13. I.E. Segal [2] : Space time decay for solutions of wave equations. Advances in Math., 22 (1976), 305-311. Zbl0344.35058MR58 #11945
  14. J. Shatah [1] : Global existence of small solutions to nonlinear evolution equations. J. diff. equations, 46 (1982), 409-425. Zbl0518.35046MR84g:35036
  15. A. Sommerfeld [1] : Vorlesungen über theoretische Physik, Bd. III u. IV, Akademische Verlagsgesellschaft, Leipzig, 1964. Zbl0041.56001
  16. W. Strauss [1]: Decay and asymptotics for □u = F(u). J. Funct. Anal. 2 (1968), 409-457. Zbl0182.13602MR38 #1385
  17. W. Strauss [2] : Everywhere defined wave equations. in “Nonlinear evolution equations”, M.G. Crandall Ed., Academic Press, 1978, 85-102. Zbl0466.47005MR82c:47078
  18. R.S. Strichartz [1] : Convolution with kernels having singularities on a sphere. Trans. A.M.S., 148 (1970), 461-471. Zbl0199.17502MR41 #876
  19. R.S. Strichartz [2] : A priori estimates for the wave equation and some applications. J. Funct. Analysis, 5 (1970), 218-235. Zbl0189.40701MR41 #2231
  20. M.E. Taylor [1] : Pseudodifferential operators. Princeton University Press, Princeton, New Jersey, 1981. Zbl0453.47026MR82i:35172
  21. W.v. Wahl [1] : Lp-decay rates for homogeneous wave equations. Math. Zeitschrift, 120 (1971), 93-106. Zbl0212.44201
  22. A. Yariv [1] : Quantum electronics, second edition. John Wiley, Sons, Inc., New York - London - Sydney - Toronto, 1975. 

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