On the Unique Solvability of the Cauchy Problem in the ClassC^1, 0 (D) for Parabolic Systems onthe Plane

The Cauchy problem for Petrovskii second-order parabolic systems in a strip on the plane is considered. The coefficients of the system satisfy the double Dini condition. The unique solvability of the problem in the space of functions that are continuous and bounded together with their first spatial derivatives in the closure of the strip is established, and the corresponding estimates are obtained. An integral representation of the solution is given.