P. Tritscher et P. Broadbridge, GRAIN-BOUNDARY GROOVING BY SURFACE-DIFFUSION - AN ANALYTIC NONLINEAR MODEL FOR A SYMMETRICAL GROOVE, Proceedings - Royal Society. Mathematical and physical sciences, 450(1940), 1995, pp. 569-587
The fourth-order nonlinear boundary-value problem for the evolution of
a single symmetric grain-boundary groove by surface diffusion is mode
lled analytically. A solution is achieved by partitioning the surface
into subintervals delimited by lines of constant slope. Within each su
binterval, the advance of the surface is described by an integrable no
nlinear evolution equation. The model is capable of incorporating the
actual nonlinearity arbitrarily closely. The surface profile is determ
ined for various values of the central groove slope including the limi
ting case of a groove which has a root that is vertical. Such a soluti
on exists only because of the nonlinearity.