Some examples of hyperbolic equations without local solvability
Annales scientifiques de l'École Normale Supérieure (1989)
- Volume: 22, Issue: 1, page 109-125
- ISSN: 0012-9593
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top- [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] 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] 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] 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] L. HÖRMANDER, Linear Partial Differential Operators, Springer Verlag, Berlin, 1963.
- [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] 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
Citations in EuDML Documents
top- Yuri V. Egorov, Sur un exemple d'équation linéaire hyperbolique n'ayant pas de solution
- Yuri Egorov, On a linear hyperbolic equation with smooth coefficients without solutions
- Ferruccio Colombini, Daniele del Santo, Tamotu Kinoshita, Well-posedness of the Cauchy problem for a hyperbolic equation with non-Lipschitz coefficients
- F. Colombini, N. Lerner, Hyperbolic operators with non Lipschitz coefficients