We prove existence and uniqueness of classical solutions for the motion of hypersurfaces driven by mean curvature and diffusion of a solute along the surface. This free boundary problem involves solving a coupled system of fully nonlinear partial differential equations.
J. Math. Anal. Appl., 234, pp. 660-674. 1999
Classical solutions for diffusion-induced grain-boundary motion
Uwe Mayer, Gieri Simonett