  In this paper, we study the motion of spirals by mean curvature type motion
in the (two dimensional) plane. Our motivation comes from dislocation dynamics;
in this context, spirals appear when a screw dislocation line reaches the
surface of a crystal. The first main result of this paper is a comparison
principle for the corresponding parabolic quasi-linear equation. As far as
motion of spirals are concerned, the novelty and originality of our setting and
results come from the fact that, first, the singularity generated by the
attached end point of spirals is taken into account for the first time, and
second, spirals are studied in the whole space. Our second main result states
that the Cauchy problem is well-posed in the class of sub-linear weak
(viscosity) solutions. We also explain how to get the existence of smooth
solutions when initial data satisfy an additional compatibility condition.

Analysis of PDEs