Nachal'no-kraevye zadachi dlya odnorodnykh parabolicheskikh sistem v poluogranichennoy ploskoy oblasti i uslovie dopolnitel'nosti

Abstract

We consider initial–boundary value problems for homogeneous parabolic systemswith coefficients satisfying the double Dini condition with zero initial conditions in a semiboundedplane domain with nonsmooth lateral boundary. The method of boundary integralequations is used to prove a theorem on the unique classical solvability of such problems in thespace of functions that are continuous together with their first spatial derivative in the closureof the domain. An integral representation of the obtained solutions is given. It is shown thatthe condition for the solvability of the posed problems considered in the paper is equivalent tothe well-known complementarity condition.