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

Chen, Gong; Jendrej, Jacek

doi:10.1090/tran/7923

Lyapunov-type characterisation of exponential dichotomies with applications to the heat and Klein–Gordon equations
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by Gong Chen and Jacek Jendrej PDF

Trans. Amer. Math. Soc. 372 (2019), 7461-7496 Request permission

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.

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