This pre-print was submitted to arXiv on 18 September 2015.In this paper we study the well-posedness of weakly hyperbolic systems\ud with time dependent coefficients. We assume that the eigenvalues are low regular,\ud in the sense that they are Holder with respect to t. In the past these kind of systems\ud have been investigated by Yuzawa [Yuz05] and Kajitani [KY06] by employing\ud semigroup techniques (Tanabe-Sobolevski method). Here, under a certain uniform\ud property of the eigenvalues, we improve the Gevrey well-posedness result of [Yuz05]\ud and we obtain well-posedness in spaces of ultradistributions as well. Our main idea\ud is a reduction of the system to block Sylvester form and then the formulation of\ud suitable energy estimates inspired by the treatment of scalar equations in [GR12]
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