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ON THE CAUCHY PROBLEM FOR NON-EFFECTIVELY HYPERBOLIC OPERATORS:: THE GEVREY 3 WELL-POSEDNESS.
- Source :
-
Journal of Hyperbolic Differential Equations . Dec2011, Vol. 8 Issue 4, p615-650. 36p. - Publication Year :
- 2011
-
Abstract
- For hyperbolic differential operators P with double characteristics we study the relations between the maximal Gevrey index for the strong Gevrey well-posedness and the Hamilton map and flow of the associated principal symbol p. If the Hamilton map admits a Jordan block of size 4 on the double characteristic manifold denoted by Σ and by assuming that the Hamilton flow does not approach Σ tangentially, we proved earlier that the Cauchy problem for P is well-posed in the Gevrey class 1 ≤ s < 4 for any lower order term. In the present paper, we remove this restriction on the Hamilton flow and establish that the Cauchy problem for P is well-posed in the Gevrey class 1 ≤ s < 3 for any lower order term and we check that the Gevrey index 3 is optimal. Combining this with results already proved for the other cases, we conclude that the Hamilton map and flow completely characterizes the threshold for the strong Gevrey well-posedness and vice versa. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02198916
- Volume :
- 8
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Journal of Hyperbolic Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 70025343
- Full Text :
- https://doi.org/10.1142/S0219891611002512