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We use the sixth order linear parabolic equation \begin{equation}\frac{\partial y}{\partial t}=B\left(\alpha\frac{\partial^{6}y}{\partialx^{6}}-\frac{\partial^{4}y}{\partial x^{4}}\right),\ x\in \mathbb{R}_{+},\t>0,\nonumber \end{equation} proposed by Rabkin and describing the evolution ofa solid surface covered with a thin, inert and fully elastic passivation layer,to analyze the grain boundary groove formation on initially flat surface. Wederive the corresponding boundary conditions and construct an asymptoticrepresentation of the solution to this initial boundary value problem when$\alpha$ is small, by applying the theory of singular perturbation. Weillustrate the effect of passivation film near and far from a grain boundarygroove.

Grain Boundary Grooving in a Bicrystal with Passivation Coating