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.
|Number of pages||36|
|Journal||Transactions of the American Mathematical Society|
|State||Published - Nov 15 2019|
Bibliographical noteFunding Information:
Part of this work was completed when the second author was visiting the University of Chicago Mathematics Department and the University of Toronto Mathematics Department. He was also partially supported by the ANR-18-CE40-0028 project ESSED.
© 2019 American Mathematical Society
- Exponential dichotomy
- Lyapunov functional
- Time-dependent potential
ASJC Scopus subject areas
- Mathematics (all)
- Applied Mathematics