In this paper we study the propagation of a phase boundary which meets the
boundary of the body at an edge or meets other phase boundaries at a juncti
on. We show that it is necessary to provide kinetic relations for the edges
and junctions in addition to the kinetic relation of the phase boundary. W
e derive thermodynamically consistent forms for these additional kinetic re
lations and show that they have a profound effect on the evolution of the p
hase boundary. (C) 1998 Elsevier Science Ltd. All rights reserved.