Initial–Boundary Value Problems for Homogeneous Parabolic Systems in a Semibounded Plane Domain and Complementarity Condition

Abstract

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