Steady-state heat distribution in bimaterial with an interface crack: Part 1

The transmission problem describing a steady-state temperature distribution in a plane consisting of two half-planes occupied by different materials with exponential internal thermal conductivities with a single finite crack along the interface is considered. The compatibility conditions for the boundary functions are formulated under which the problem has a unique classical solution. Closed-form representations of the classical solution are found. The weak solution to the problem is studied without making additional assumptions, and asymptotic expansions are constructed for the weak solution and its first derivatives near the ends of the crack.