GARETTO, C. and RUZHANSKY, M., 2015. On hyperbolic systems with time dependent Holder characteristics. arXiv:1509.01603v2 [math.AP].
In this paper we study the well-posedness of weakly hyperbolic systems
with time dependent coefficients. We assume that the eigenvalues are low regular,
in the sense that they are Holder with respect to t. In the past these kind of systems
have been investigated by Yuzawa [Yuz05] and Kajitani [KY06] by employing
semigroup techniques (Tanabe-Sobolevski method). Here, under a certain uniform
property of the eigenvalues, we improve the Gevrey well-posedness result of [Yuz05]
and we obtain well-posedness in spaces of ultradistributions as well. Our main idea
is a reduction of the system to block Sylvester form and then the formulation of
suitable energy estimates inspired by the treatment of scalar equations in [GR12].
This pre-print was submitted to arXiv on 18 September 2015.