Abstract
The short-time and global behavior are studied for an autonomous linear evolution equation, which is defined by a generator inducing a uniformly bounded holomorphic semigroup in a Hilbert space. A general necessary and sufficient condition is introduced under which the norm of the solution is shown to be a log-convex and strictly decreasing function of time, and differentiable also at the initial time with a derivative controlled by the lower bound of the generator, which moreover is shown to be positively accretive. Injectivity of holomorphic semigroups is the main technical tool.
Original language | English |
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Journal | Electronic Research Archive (ERA) |
Volume | 25 |
Pages (from-to) | 72-86 |
Number of pages | 15 |
ISSN | 1935-9179 |
DOIs | |
Publication status | Published - 2018 |
Keywords
- log-convex decay
- non-selfadjoint
- hyponormal
- positively accretive operators
- short-time behavior