Quasianalytic and nonquasianalytic solutions for a class of weakly hyperbolic Cauchy problems

In the weakly hyperbolic Cauchy problem, we investigate the relation between the modulus of continuity in the time variable of the coefficients and the well-posedness in Beurling–Roumieu classes of ultradifferentiable functions and functionals. We find a sharp condition on the modulus of continuity assuring the well-posedness in nonquasianalytic classes.