Copyright © 2010 Yu Lin et al. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider the propagator of an evolution equation, which is a semigroup of linear
operators. Questions related to its operator norm function and its behavior at the
critical point for norm continuity or compactness or differentiability are studied.