Steady-state heat distribution in bimaterial with an interface crack: Part 2

The problem of a steady-state heat distribution in a domain consisting of two subdomains filled with different inhomogeneous materials is considered. Mathematically, the conditions on the boundary of the subdomains modeling heat transfer and a heat flux through their common boundary are transmission conditions. Additionally, the boundary conditions model a crack on the boundary of the subdomains, which leads to inhomogeneities in the boundary conditions. The problem is studied by constructing its solution using the Green's function with the help of the WKB method and by comparing the singularities of the solution components with those of a specially chosen problem with constant coefficients and boundary functions of special form.