Geodesic
Cauchy problem in multi-anisotropic Gevrey classes for weakly hyperbolic operators
Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 1, pp. 21-50

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We prove the well-posedness of the Cauchy Problem for first order weakly hyperbolic systems in the multi-anisotropic Gevrey classes, that generalize the standard Gevrey spaces. The result is obtained under the following hypotheses: the principal part is weakly hyperbolic with constant coefficients, the lower order terms satisfy some Levi-type conditions; and lastly the coefficients of the lower order terms belong to a suitable anisotropic Gevrey class. In the proof it is used the quasi-symmetrization of Sylvster-type systems, adapted to the case of the multi-anisotropic Gevrey classes and taking into account the lower order terms. 
@article{BUMI_2006_8_9B_1_a1,
     author = {Calvo, Daniela},
     title = {Cauchy problem in multi-anisotropic {Gevrey} classes for weakly hyperbolic operators},
     journal = {Bollettino della Unione matematica italiana},
     pages = {21--50},
     publisher = {mathdoc},
     volume = {Ser. 8, 9B},
     number = {1},
     year = {2006},
     zbl = {1178.35236},
     mrnumber = {MR2204898},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2006_8_9B_1_a1/}
}
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Calvo, Daniela. Cauchy problem in multi-anisotropic Gevrey classes for weakly hyperbolic operators. Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 1, pp. 21-50. http://geodesic.mathdoc.fr/item/BUMI_2006_8_9B_1_a1/