On hyperbolic systems with time dependent Holder characteristics

2016-01-14T15:23:02Z (GMT) by Claudia Garetto Michael Ruzhansky
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].