Characterisation of Log-Convex Decay in Non-Selfadjoint Dynamics
Analysis of PDEs
2018-12-18 v4
Abstract
The short-time and global behaviour 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.
Keywords
Cite
@article{arxiv.1806.10870,
title = {Characterisation of Log-Convex Decay in Non-Selfadjoint Dynamics},
author = {Jon Johnsen},
journal= {arXiv preprint arXiv:1806.10870},
year = {2018}
}
Comments
11 pages. Version to appear in Electronic Research Announcements in Mathematical Sciences (a precision in Lemma 3.2, plus minor improvements)