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## Banach Center Publications

1996 | 33 | 1 | 61-66
Tytuł artykułu

### On a linear hyperbolic equation with smooth coefficients without solutions

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
An example of a locally unsolvable hyperbolic equation of the second order is constructed, which has smooth ($C^∞$) coefficients, but has no solutions in the class of distributions.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
61-66
Opis fizyczny
Daty
wydano
1996
Twórcy
autor
• Université Paul Sabatier, UFR MIG, Labo MIP, Route de Narbonne, 118, 31062 Toulouse, France
Bibliografia
• [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.
• [2] M. M. Smirnov, Degenerating Elliptic and Hyperbolic Equations, Nauka, Moscow, 1966 (in Russian).
• [3] V. Ya. Ivriĭ and V. Petkov, Necessary conditions for the Cauchy problem for non-strictly hyperbolic equations to be well-posed, Russian Math. Surveys 29 (1974), 1-70.
• [4] O. A. Oleĭnik, On the Cauchy problem for weakly hyperbolic equations, Comm. Pure Appl. Math. 23 (1970), 569-586.
• [5] H. Lewy, An example of a smooth linear partial differential equation without solution, Ann. of Math. 66 (1957), 155-158.
• [6] L. Hörmander, Linear Partial Differential Operators, Springer, 1976.
• [7] L. Nirenberg and F. Trèves, On local solvability of linear partial differential operators, I. Necessary conditions, Comm. Pure Appl. Math. 23 (1970), 1-38.
• [8] Yu. V. Egorov, On the local solvability of the differential equations with simple characteristics, Russian Math. Surveys 26 (1971), 183-198.
• [9] Yu. V. Egorov, Linear Differential Equations of Principal Type, Plenum, 1986.
• [10] L. Hörmander, The Analysis of Linear Partial Differential Operators, Vol. III, Springer, 1985.
• [11] Y. Kannai, An unsolvable hypoelliptic diferential operator, Israel Math. J. 9 (1971), 306-315.
• [12] F. Colombini and S. Spagnolo, Some examples of hyperbolic equations without local solvability, Ann. Sci. Ecole Norm. Sup. 22 (1989), 109-125.
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Bibliografia
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