On the well-posedness of weakly hyperbolic equations with time dependent   coefficients
  In this paper we analyse the Gevrey well-posedness of the Cauchy problem for weakly hyperbolic equations of general form with time-dependent coefficients. The results involve the order of lower order terms and the number of multiple roots. We also derive the corresponding well-posedness results in the space of Gevrey Beurling ultradistributions. 
Claudia Garetto and Michael Ruzhansky
math.AP