On an example of a linear hyperbolic equation having no solution

Yuri V. Egorov

Journées équations aux dérivées partielles (1992)

  • page 1-6
  • ISSN: 0752-0360

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Egorov, Yuri V.. "Sur un exemple d'équation linéaire hyperbolique n'ayant pas de solution." Journées équations aux dérivées partielles (1992): 1-6. <http://eudml.org/doc/93245>.

@article{Egorov1992,
author = {Egorov, Yuri V.},
journal = {Journées équations aux dérivées partielles},
keywords = {weakly hyperbolic equations},
language = {fre},
pages = {1-6},
publisher = {Ecole polytechnique},
title = {Sur un exemple d'équation linéaire hyperbolique n'ayant pas de solution},
url = {http://eudml.org/doc/93245},
year = {1992},
}

TY - JOUR
AU - Egorov, Yuri V.
TI - Sur un exemple d'équation linéaire hyperbolique n'ayant pas de solution
JO - Journées équations aux dérivées partielles
PY - 1992
PB - Ecole polytechnique
SP - 1
EP - 6
LA - fre
KW - weakly hyperbolic equations
UR - http://eudml.org/doc/93245
ER -

References

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  1. [1] M.H. Protter, The Cauchy problem for a hyperbolic second order equation with data on the parabolic line, Canad. J. Math., 6, 1954, 542-553. Zbl0057.08101MR16,255d
  2. [2] M.M. Smirnov, Degenerating elliptic and hyperbolic equations, Nauka, Moscow, 1966. 
  3. [3] V.Ya. Ivrii, V. Petkov, Necessary conditions for the Cauchy problem for non-strictly hyperbolic equations to be well-posed, Russian Math. Surveys, 29, 1974, 1-70. Zbl0312.35049
  4. [4] O.A. Oleinik, On the Cauchy problem for weakly hyperbolic equation, Comm. Pure Appl. Math., 23, 1970, 569-586. MR41 #8823
  5. [5] H. Lewy, An example of a smooth linear partial differential equation without solution, Ann. of Math., 66, 1957, 155-158. Zbl0078.08104MR19,551d
  6. [6] L. Hörmander, Linear partial differential operators, Springer, 1976. Zbl0321.35001
  7. [7] L. Nirenberg, F. Trèves, On local solvability of linear partial differential operators I. Necessary conditions, Comm. Pure Appl. Math., 23, 1970, 1-38. Zbl0191.39103MR41 #9064a
  8. [8] Yu.V. Egorov, Sur la solvabilité des équations différentielles à caractéristiques doubles, Russian Math. Surveys, 26, 1971, 183-198. 
  9. [9] Yu.V. Egorov, Linear differential equations of principal type, Plenum Press, 1986. Zbl0669.35001
  10. [10] L. Hörmander, The analysis of linear partial differential operators III, Springer, 1985. Zbl0601.35001
  11. [11] Y. Kannai, An unsolvable hypoelliptic diferential operator, Israel Math. J., 9, 1971, 306-315. Zbl0211.40601MR43 #2573
  12. [12] F. Colombini, S. Spagnolo, Some examples of hyperbolic equations without local solvability, Ann. Sci. de l'Ecole Normale Supérieure de Paris, 12, 1989, 109-125. Zbl0702.35146MR90d:35164
  13. [13] F. Colombini, E. Jannelli, S. Spagnolo, Non-uniqueness in hyperbolic Cauchy problems, Annals of Mathematics, 126, 1987, 495-524. Zbl0649.35051MR89e:35086

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