On the blow-up rate for fast blow-up solutions arising in an anisotropic crystalline motion

摘要

We consider the asymptotic behavior of motion of polygonal convex curves by crystalline curvature in the plane. There appear spontaneously two types of singularity: one is single point extinction and the other is degenerate pinching. We mainly discuss degenerate pinching singularity and show the exact blow-up rate for a fast blow-up solution which arises in an equivalent blow-up problem.