Advances in Difference Equations
Volume 2010 (2010), Article ID 795484, 8 pages
doi:10.1155/2010/795484
Notes on the propagators of evolution equations
Yu Lin1
, Ti-Jun Xiao2
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
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.