Well-posedness of hyperbolic systems with multiplicities and smooth coefficients

2016/03/11 by Garetto, Claudia, Jäh, Christian
#35L45 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1603.03602

Abstract

We study hyperbolic systems with multiplicities and smo\-oth coefficients. In the case of non-analytic, smooth coefficients, we prove well-posedness in any Gevrey class and when the coefficients are analytic, we prove C^∞ well-posedness. The proof is based on a transformation to block Sylvester form introduced by D'Ancona and Spagnolo in Ref. 9 which increases the system size but does not change the eigenvalues. This reduction introduces lower order terms for which appropriate Levi-type conditions are found. These translate then into conditions on the original coefficient matrix. This paper can be considered as a generalisation of Ref. 12, where weakly hyperbolic higher order equations with lower order terms were considered.

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