On the Unique Solvability of Initial-Boundary Value Problems for Parabolic Systems in Bounded Plane Domains with Nonsmooth Lateral Boundaries

We consider the first and second initial-boundary value problems for inhomogeneoussecond-order parabolic systems with Dini continuous coefficients under nonzero initial conditionsin bounded domains on the plane with nonsmooth lateral boundaries that, in particular, admitcusps. Theorems are proved on the unique classical solvability of these problems in the space offunctions that are continuous together with their first spatial derivatives in the closure of thesedomains.