Smooth solution of the second initial-boundary value problem for a model parabolic system in a semibounded nonsmooth domain on the plane

The second initial-boundary value problem for a second-order Petrovskii parabolic system with constant coefficients in a semibounded plane domain with a nonsmooth lateral boundary is considered. The uniqueness of a solution to this problem in the class $C^{2,1}(\Omega)\cap\underset 0{C}^{1,0}(\bar\Omega)$ is proved. The minimum condition on the boundary function under which the solution of the problem belongs to $\underset 0{C}^{2,1}(\bar\Omega)$ is investigated. A constructive solution is obtained by applying the boundary integral equation method.