Abstract
Diffusion in the presence of high-diffusivity paths is an important issue of current technology. In metals high-diffusivity paths are identified with dislocations, grain boundaries, free surfaces and internal microcracks. Diffusion in a media with two distinct families of diffusion paths is modelled by two coupled linear partial differential equations of parabolic type with diffusivities D 1 and D 2. Physically the situation D 2 ⪡ D 1 is of some considerable interest and previously established results, for D 2 non-zero, for the solution of boundary value problems, are not applicable to the idealized theory characterized by D 2 vanishing. An integral equation, which arises in the solution of boundary value problems for this idealized theory, is formally solved.
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