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Sur un exemple d'équation linéaire hyperbolique n'ayant pas de solution
[On an example of a linear hyperbolic equation having no solution]
Yuri V. Egorov
Journées équations aux dérivées partielles (1992), article no. 14, 6 p.
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MR: 93a:35004d
DOI: 10.5802/jedp.432
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@article{JEDP_1992____A14_0,
     author = {Yuri V. Egorov},
     title = {Sur un exemple d'\'equation lin\'eaire hyperbolique n'ayant pas de solution},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {14},
     publisher = {\'Ecole polytechnique},
     year = {1992},
     doi = {10.5802/jedp.432},
     mrnumber = {93a:35004d},
     language = {fr},
     url = {https://jedp.centre-mersenne.org/articles/10.5802/jedp.432/}
}
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Yuri V. Egorov. 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. https://jedp.centre-mersenne.org/articles/10.5802/jedp.432/
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[2] M.M. Smirnov, Degenerating elliptic and hyperbolic equations, Nauka, Moscow, 1966.

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[4] O.A. Oleinik, On the Cauchy problem for weakly hyperbolic equation, Comm. Pure Appl. Math., 23, 1970, 569-586. | MR: 41 #8823 | Zbl: 0193.38602

[5] H. Lewy, An example of a smooth linear partial differential equation without solution, Ann. of Math., 66, 1957, 155-158. | MR: 19,551d | Zbl: 0078.08104

[6] L. Hörmander, Linear partial differential operators, Springer, 1976. | Zbl: 0321.35001

[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: 41 #9064a | Zbl: 0191.39103

[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: 0669.35001

[10] L. Hörmander, The analysis of linear partial differential operators III, Springer, 1985. | Zbl: 0601.35001

[11] Y. Kannai, An unsolvable hypoelliptic diferential operator, Israel Math. J., 9, 1971, 306-315. | MR: 43 #2573 | Zbl: 0211.40601

[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: 90d:35164 | Zbl: 0702.35146

[13] F. Colombini, E. Jannelli, S. Spagnolo, Non-uniqueness in hyperbolic Cauchy problems, Annals of Mathematics, 126, 1987, 495-524. | MR: 89e:35086 | Zbl: 0649.35051

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