Theory of Curvature and Grooving Effects in DIGM - II: the Mathematics
O Penrose, John W. Cahn
We examine and solve the mathematical problems that arise when diffusion induced grain boundary motion is formulated as a free boundary problem, i.e. as a system of partial differential equations on a moving curved interface with surface grooving as a boundary condition. We confirm that there are two types of solutions, termed trailing and connecting. A more careful derivation of the basic equations leads to a higher order term which can become important in the trailing solution. Our results are more precise and give greater detail about the shape and the composition than the approximate results in a companion paper.