Poisson Potential in the First Initial–Boundary Value Problem for a Parabolic System in a Semibounded Domain on the Plane

We consider the first initial–boundary value problem for a parabolic system in a semibounded domain on the plane with nonsmooth lateral boundary that may have cusps. The continuity of the trace of the Poisson potential on such a boundary is studied, and a theorem on the existence of a classical solution of the problem is proved for the case of an inhomogeneous parabolic system and a nonzero initial condition.