On the Unique Solvability of Initial–Boundary Value Problemsfor Parabolic Systems in a Plane Bounded Domain with General BoundaryConditions

An initial–boundary value problem is considered for an inhomogeneous parabolic system with Dini-continuous coefficients with a nonzero initial condition in a plane bounded domain with nonsmooth lateral boundaries allowing the presence of “cusps” on which general boundary conditions are given for the components of the sought vector function. Theorems on the existence and uniqueness of the classical solution to the problem from the space of vector functions that are continuous with their spatial derivatives of the first order in the closure of the domain are proved. An integral representation is given, and the smoothness of the obtained solution is investigated.