Dj. Arrigo et al., THE DEPTH OF A STEEP EVAPORATING GRAIN-BOUNDARY GROOVE - APPLICATION OF COMPARISON-THEOREMS, Mathematical and computer modelling, 25(10), 1997, pp. 1-8
The nonlinear Mullins diffusion equation for the development of a surf
ace groove by evaporation-condensation is reconsidered. Comparison the
orems for differential equations are employed to obtain upper and lowe
r bounds on the profile of the groove itself and on the growth rate of
the groove at the grain boundary It is shown that as the dihedral ang
le at the grain boundary approaches zero, the groove growth rate diver
ges logarithmically. This phenomenon is in disparity with the finite g
rowth rate found in the development of grooves by surface diffusion.