On the unambiguous solvability of initial boundary value problems for parabolic systems in a semi-bounded flat region with a nonsmooth lateral boundary

We consider the initial boundary value problem for an inhomogeneous parabolic system with Dini-continuous coefficients with a nonzero initial condition in a semi-constrained flat region with a nonsmooth lateral boundary admitting beaks, on which boundary conditions of general form are set. We prove a theorem on the single-valued solvability of such a problem in the space of functions continuous and bounded together with their spatial derivative of the first order in the closure of the region. An integral representation is given and the smoothness character of the obtained solution is investigated.