Exact solution of integro-differential equations of diffusion along a grain boundary

We analyse model problems of stress-induced atomic diffusion from a point s ource or from the surface of a material into an infinite or semi-infinite g rain boundary, respectively. The problems are formulated in terms of partia l differential equations which involve singular integral operators. The sel f-similarity of these equations leads to singular integro-differential equa tions which are solved in closed form by reduction to an exceptional case o f the Riemann-Hilbert boundary-value problem of the theory of analytic func tions on an open contour. We also give a series representation and a full a symptotic expansion of the solution in the case of large arguments. Numeric al results are reported.