Exact solvability of the Mullins nonlinear diffusion model of groove development

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Abstract
The Mullins equation for the development of a surface groove by evaporation–condensation is yt=yxx/1+y2x. It is pointed out that this is the equation of the potential for the field variable Θ satisfying the nonlinear diffusion equation Θt=∂x[Θx/1+Θ2]. The latter has already been solved exactly, with boundary conditions corresponding exactly to those specified by Mullins. The depth of a groove at a grain boundary is predicted exactly without first making the linear (small‐slope) approximation. For some types of initial data, the Cauchy problem may be solved for some related equations.