Uniqueness of solutions of initial-boundary value problems for parabolic systems with Dini-continuous coefficients in domains on the plane

The first and second initial-boundary value problems for Petrovskii parabolic systems of the second order with coefficients satisfying the Dini condition in plane domains with nonsmooth lateral boundaries admitting, in particular, cusps are considered. Theorems on the uniqueness of classical solutions of these problems in the class of functions that are continuous and bounded together with their first spatial derivatives in the closure of these domains are proved.