On the Smoothness of the Poisson Potential for Second-Order Parabolic Systems on the Plane

We consider the solution of the Cauchy problem in a strip on the plane for a homogeneous second-order parabolic system. The coefficients of the system satisfy the double Dini condition. The initial function is continuous and bounded along with its first and second derivatives. Using the Poisson potential, the nature of the smoothness of this solution is studied and the corresponding estimates are proved.