Some examples of hyperbolic equations without local solvability

F. Colombini; S. Spagnolo

Annales scientifiques de l'École Normale Supérieure (1989)

  • Volume: 22, Issue: 1, page 109-125
  • ISSN: 0012-9593

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Colombini, F., and Spagnolo, S.. "Some examples of hyperbolic equations without local solvability." Annales scientifiques de l'École Normale Supérieure 22.1 (1989): 109-125. <http://eudml.org/doc/82242>.

@article{Colombini1989,
author = {Colombini, F., Spagnolo, S.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {hyperbolic equations; local solvability; Hölder continuous coefficients},
language = {eng},
number = {1},
pages = {109-125},
publisher = {Elsevier},
title = {Some examples of hyperbolic equations without local solvability},
url = {http://eudml.org/doc/82242},
volume = {22},
year = {1989},
}

TY - JOUR
AU - Colombini, F.
AU - Spagnolo, S.
TI - Some examples of hyperbolic equations without local solvability
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1989
PB - Elsevier
VL - 22
IS - 1
SP - 109
EP - 125
LA - eng
KW - hyperbolic equations; local solvability; Hölder continuous coefficients
UR - http://eudml.org/doc/82242
ER -

References

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  1. [1] F. COLOMBINI, E. DE GIORGI and S. SPAGNOLO, Sur les équations hyperboliques avec des coefficients qui ne dépendent que du temps (Ann. Sc. Norm. Sup. Pisa, Vol. 6, 1979, pp. 511-559). Zbl0417.35049MR81c:35077
  2. [2] F. COLOMBINI, E. JANNELLI and S. SPAGNOLO, Well-Posedness in the Gevrey Classes of the Cauchy Problem for a Non-strictly Hyperbolic Equation with Coefficients Depending on Time (Ann. Sc. Norm. Sup. Pisa, Vol. 10, 1983, pp. 291-312). Zbl0543.35056MR85f:35131
  3. [3] F. COLOMBINI, E. JANNELLI and S. SPAGNOLO, Non-Uniqueness in Hyperbolic Cauchy Problems (Ann. of Math., Vol. 126, 1987, pp. 495-524). Zbl0649.35051MR89e:35086
  4. [4] F. COLOMBINI and S. SPAGNOLO, An Example of Weakly Hyperbolic Cauchy Problem Not Well-Posed in C∞ (Acta Math., Vol. 148, 1982, pp. 243-253). Zbl0517.35053MR83m:35085
  5. [5] L. HÖRMANDER, Linear Partial Differential Operators, Springer Verlag, Berlin, 1963. 
  6. [6] L. HÖRMANDER, Propagation of Singularities and Semi-Global Existence Theorems for (Pseudo-) Differential Operators of Principal Type (Ann. of Math., Vol. 108, 1978, pp. 569-609). Zbl0396.35087
  7. [7] L. NIRENBERG and F. TREVES, On Local Solvability of Linear Partial Differential Equations. I. Necessary Conditions. II. Sufficient Conditions. Correction (Comm. Pure Appl. Math., Vol. 23, 1970, pp. 1-38 and pp. 459-509 ; Vol. 24, 1971, pp. 279-288). Zbl0208.35902

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