Cauchy problem in multi-anisotropic Gevrey classes for weakly hyperbolic operators

Daniela Calvo

Bollettino dell'Unione Matematica Italiana (2006)

  • Volume: 9-B, Issue: 1, page 21-50
  • ISSN: 0392-4041

Abstract

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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.

How to cite

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Calvo, Daniela. "Cauchy problem in multi-anisotropic Gevrey classes for weakly hyperbolic operators." Bollettino dell'Unione Matematica Italiana 9-B.1 (2006): 21-50. <http://eudml.org/doc/289602>.

@article{Calvo2006,
abstract = { 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.},
author = {Calvo, Daniela},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {21-50},
publisher = {Unione Matematica Italiana},
title = {Cauchy problem in multi-anisotropic Gevrey classes for weakly hyperbolic operators},
url = {http://eudml.org/doc/289602},
volume = {9-B},
year = {2006},
}

TY - JOUR
AU - Calvo, Daniela
TI - Cauchy problem in multi-anisotropic Gevrey classes for weakly hyperbolic operators
JO - Bollettino dell'Unione Matematica Italiana
DA - 2006/2//
PB - Unione Matematica Italiana
VL - 9-B
IS - 1
SP - 21
EP - 50
AB - 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.
LA - eng
UR - http://eudml.org/doc/289602
ER -

References

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