Advances in Difference Equations
Volume 2010 (2010), Article ID 795484, 8 pages
doi:10.1155/2010/795484
Research Article

Notes on the Propagators of Evolution Equations

Yu Lin,1 Ti-Jun Xiao,2 and Jin Liang3

1Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
2Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai 200433, China
3Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China

Received 8 January 2010; Accepted 1 February 2010

Academic Editor: Gaston Mandata N'Guerekata

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.

Abstract

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.