  We study, both analytically and numerically, the dynamics of elastic
boundaries such as crack fronts in fracture and surfaces of contact in solid on
solid friction. The elastic waves in the solid give rise to kinks that move
with a characteristic velocity along the boundary. As stopping kinks pass
through they cause moving parts of the boundary to stop. Starting kinks cause
stationary parts of the boundary to move. We study the interaction of these
kinks with disorder that arises from the spatial variations of the friction
constant or fracture energy. In the absence of elastic waves, elastic
boundaries with disorder operate at a critical point leading to a power-law
distribution of slip events and self-affine boundaries. Elastic waves result in
relevant perturbations at this fixed point. Slip events beyond a critical size
run away and the velocity of the boundary jumps to a nonzero value when the
external load is increased above a threshold. We analyze in detail a class of
simple models that capture the essential features of bulk vectorial elasticity
and discuss the implications of our results for friction and fracture dynamics.
