Abstract <p>An initial-boundary value problem is considered for an inhomogeneous parabolic system with Dini-continuous coefficients and a nonzero initial condition in a semibounded plane domain with a cusp-admitting nonsmooth lateral boundary on which general boundary conditions are given. A theorem is proved on the unique solvability of this problem in the space of functions that are continuous and bounded together with their first spatial derivatives in the closure of the domain. An integral representation of the resulting solution is given, and the character of its smoothness is studied.</p>