Classical Solutions of the First Boundary Value Problem for Parabolic Systems on the Plane

The first boundary value problem for a second-order parabolic system with one spatial variable in a domain with nonsmooth lateral boundaries is considered. The domain can be bounded or semi-bounded. The coefficients of the system depend only on the spatial variable and satisfy the Hölder condition. The initial and boundary functions are assumed to be continuous and bounded. The existence and uniqueness of a classical solution of this problem is established.