Heat distribution on a plane which consists of two different non-homogeneous materials with a simi-bounded interphase crack

The problem of transmission for the system of equations is considered. It describes the stationary distribution of heat in the plane consisting of two half-planes, filled with non-homogeneous materials with different exponential coefficients of thermal conductivity. There is a semi-bounded crack on the boundary of these materials. A definition of the classical solution of this problem is given and the conditions of its existence are formulated. Explicit formulas of this solution are worked out. This research developed the results which are obtained for the bounded crack and they are the basis for further study of asymptotic representations of the solution and its first derivatives near the bounded crack. Bibliogr. 19.