Abstract
We give a sufficient condition for the existence of an exponential dichotomy for a general linear dynamical system (not necessarily invertible) in a Banach space, in discrete or continuous time. We provide applications to the backward heat equation with a potential varying in time, and to the heat equation with a finite number of slowly moving potentials. We also consider the Klein-Gordon equation with a finite number of potentials whose centres move at sublight speed with small accelerations.
Original language | English |
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Pages (from-to) | 7461-7496 |
Number of pages | 36 |
Journal | Transactions of the American Mathematical Society |
Volume | 372 |
Issue number | 10 |
DOIs | |
State | Published - Nov 15 2019 |
Bibliographical note
Publisher Copyright:© 2019 American Mathematical Society
Keywords
- Exponential dichotomy
- Lyapunov functional
- Time-dependent potential
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics