Uniqueness of solutions to initial boundary value problems for parabolic systems in plane bounded domains with nonsmooth lateral boundaries

We consider initial boundary value problems with boundary conditions of the first or second kind for one-dimensional (with respect to a spatial variable) Petrovskii parabolic systems of the second order with variable coefficients in a bounded domain with nonsmooth lateral boundaries. The uniqueness of regular solutions to these problems in the class of functions that are continuous in the closure of the domain together with their first spatial derivatives is established using the boundary integral equation method.