Lyapunov-type characterisation of exponential dichotomies with applications to the heat and Klein-Gordon equations

Gong Chen, Jacek Jendrej

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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 languageEnglish
Pages (from-to)7461-7496
Number of pages36
JournalTransactions of the American Mathematical Society
Volume372
Issue number10
DOIs
StatePublished - 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

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