Groove growth by surface subdiffusion

• The problem of the groove growth is solved in the case of the surface subdiffusion.
• An exact self-similar solution is obtained.
• Basic properties of the solution are described.
• Geometrical properties of the groove profile are calculated.

The investigation of the grain-boundary groove growth by normal surface diffusion was first done by Mullins. However, the diffusion on a solid surface is often anomalous. Recently, the groove growth in the case of surface superdiffusion has been analyzed. In the present paper, the problem of the groove growth is solved in the case of the surface subdiffusion. An exact self-similar solution is obtained and represented in terms of the Fox H-function. Basic properties of the solution are described.