HEAT DISTRIBUTION ON A PLANE WHICH CONSISTS OF TWO DIFFERENT NON-HOMOGENEOUS MATERIALS WITH A SEMI-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 nonhomogeneous 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 develops 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.