Sur un exemple d'équation linéaire hyperbolique n'ayant pas de solution
Journées équations aux dérivées partielles (1992), article no. 14, 6 p. 
@incollection{JEDP_1992____A14_0,
     author = {Egorov, Yuri V.},
     title = {Sur un exemple d'\'equation lin\'eaire hyperbolique n'ayant pas de solution},
     booktitle = {},
     series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {14},
     pages = {1--6},
     year = {1992},
     publisher = {Ecole polytechnique},
     doi = {10.5802/jedp.432},
     mrnumber = {93a:35004d},
     language = {fr},
     url = {https://www.numdam.org/articles/10.5802/jedp.432/}
}
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
SP  - 1
EP  - 6
PB  - Ecole polytechnique
UR  - https://www.numdam.org/articles/10.5802/jedp.432/
DO  - 10.5802/jedp.432
LA  - fr
ID  - JEDP_1992____A14_0
ER  - 
%0 Journal Article
%A Egorov, Yuri V.
%T Sur un exemple d'équation linéaire hyperbolique n'ayant pas de solution
%J Journées équations aux dérivées partielles
%D 1992
%P 1-6
%I Ecole polytechnique
%U https://www.numdam.org/articles/10.5802/jedp.432/
%R 10.5802/jedp.432
%G fr
%F JEDP_1992____A14_0
Egorov, Yuri V. Sur un exemple d'équation linéaire hyperbolique n'ayant pas de solution. Journées équations aux dérivées partielles (1992), article  no. 14, 6 p.. doi: 10.5802/jedp.432

[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. | MR | Zbl

[2] M.M. Smirnov, Degenerating elliptic and hyperbolic equations, Nauka, Moscow, 1966.

[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. | Zbl

[4] O.A. Oleinik, On the Cauchy problem for weakly hyperbolic equation, Comm. Pure Appl. Math., 23, 1970, 569-586. | MR | Zbl

[5] H. Lewy, An example of a smooth linear partial differential equation without solution, Ann. of Math., 66, 1957, 155-158. | MR | Zbl

[6] L. Hörmander, Linear partial differential operators, Springer, 1976. | Zbl

[7] L. Nirenberg, F. Trèves, On local solvability of linear partial differential operators I. Necessary conditions, Comm. Pure Appl. Math., 23, 1970, 1-38. | MR | Zbl

[8] Yu.V. Egorov, Sur la solvabilité des équations différentielles à caractéristiques doubles, Russian Math. Surveys, 26, 1971, 183-198.

[9] Yu.V. Egorov, Linear differential equations of principal type, Plenum Press, 1986. | Zbl

[10] L. Hörmander, The analysis of linear partial differential operators III, Springer, 1985. | Zbl

[11] Y. Kannai, An unsolvable hypoelliptic diferential operator, Israel Math. J., 9, 1971, 306-315. | MR | Zbl

[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. | Numdam | MR | Zbl

[13] F. Colombini, E. Jannelli, S. Spagnolo, Non-uniqueness in hyperbolic Cauchy problems, Annals of Mathematics, 126, 1987, 495-524. | MR | Zbl

Cité par Sources :