Supplementary Materials for “dynamics for Systems of Screw Dislocations”

In Subsection 2.1 we have discussed uniqueness only in the special case in which f is discontinuous across a (d − 1)-dimensional hypersurface. The case when two or more such (d− 1)-dimensional hypersurfaces meet is significantly more involved and can lead to non-uniqueness of solutions for Filippov systems (see, e.g., [16]). In our setting, this situation arises at points in the set Eint defined in (2.27). Indeed, in Theorem 2.20 we assumed that Z1 does not belong to the intersection of two hypersurfaces (see (2.27) and (2.28)). In this section we study fine cross-slip in the case in which Z1 belongs to Eint. For simplicity, we consider only the case in which only two hypersurfaces intersect at a point. See Figure 5.