Abstract
We study the contraction of a convex immersed plane curve along its normal vector direction with speed function 1/α κ <sup>α</sup> , where κ > 0 is the curvature of the evolving curve and α > 1 is a constant. We show that the blow-up rate of the curvature is always of type one and the rescaled solution will converge to a limit that may or may not be degenerate.