# On a linear hyperbolic equation with smooth coefficients without solutions

Banach Center Publications (1996)

- Volume: 33, Issue: 1, page 61-66
- ISSN: 0137-6934

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topEgorov, Yuri. "On a linear hyperbolic equation with smooth coefficients without solutions." Banach Center Publications 33.1 (1996): 61-66. <http://eudml.org/doc/262569>.

@article{Egorov1996,

abstract = {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.},

author = {Egorov, Yuri},

journal = {Banach Center Publications},

keywords = {locally unsolvable hyperbolic equation},

language = {eng},

number = {1},

pages = {61-66},

title = {On a linear hyperbolic equation with smooth coefficients without solutions},

url = {http://eudml.org/doc/262569},

volume = {33},

year = {1996},

}

TY - JOUR

AU - Egorov, Yuri

TI - On a linear hyperbolic equation with smooth coefficients without solutions

JO - Banach Center Publications

PY - 1996

VL - 33

IS - 1

SP - 61

EP - 66

AB - 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.

LA - eng

KW - locally unsolvable hyperbolic equation

UR - http://eudml.org/doc/262569

ER -

## References

top- [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. Zbl0057.08101
- [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. Zbl0078.08104
- [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. Zbl0191.39103
- [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. Zbl0601.35001
- [11] Y. Kannai, An unsolvable hypoelliptic diferential operator, Israel Math. J. 9 (1971), 306-315. Zbl0211.40601
- [12] F. Colombini and S. Spagnolo, Some examples of hyperbolic equations without local solvability, Ann. Sci. Ecole Norm. Sup. 22 (1989), 109-125. Zbl0702.35146

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