GARETTO, C. and JAH, C., 2016. Well-posedness of hyperbolic systems with multiplicities and smooth coefficients. arXiv:1603.03602 [math.AP]
In this paper we study hyperbolic systems with multiplicities and smooth coefficients. In the case of non-analytic 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 reduction to block Sylvester form introduced by D'Ancona and Spagnolo in Ref. 8 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 coefficients matrix. This paper can be considered as a generalisation of Ref. 11 where weakly hyperbolic higher order equations with lower order terms were considered.
This pre-print was submitted to arXiv on 11th March 2016