We consider a sharp interface model which describes diffusion-induced grain-boundary motion in a poly-crystalline material. This model leads to a fully nonlinear coupled system of partial differential equations. We show existence and uniqueness of smooth solutions.
Nonlinear Partial Differential Equations, Gui-Qiang Chen and Emmanuele DiBenedetto (editors), Amer. Math. Soc., Providence, RI, pp. 231-240, 1999
On diffusion-induced grain-boundary motion
Uwe Mayer, Gieri Simonett