Singularities of Solutions to the Cauchy Problem for a Class of Second-Order Hyperbolic Operators

In this paper we deal with the Cauchy problem for second-order hyperbolic operators with the coefficients of their principal parts depending only on the time variable. We shall give outer estimates of the wave front sets of solutions to the Cauchy problem when the Cauchy problem is C∞ well-posed. More precisely, we shall show that the wave front sets of solutions are included in the union of broken null bicharacteristics emanating from the singularities of data in non-trivial cases.