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Asymptotics for periodic systems

Tutkimustuotosvertaisarvioitu

Yksityiskohdat

AlkuperäiskieliEnglanti
Sivut7152-7172
JulkaisuJournal of Differential Equations
Vuosikerta266
Numero11
Varhainen verkossa julkaisun päivämäärä2018
DOI - pysyväislinkit
TilaJulkaistu - toukokuuta 2019
OKM-julkaisutyyppiA1 Alkuperäisartikkeli

Tiivistelmä

This paper investigates the asymptotic behaviour of solutions of periodic evolution equations. Starting with a general result concerning the quantified asymptotic behaviour of periodic evolution families we go on to consider a special class of dissipative systems arising naturally in applications. For this class of systems we analyse in detail the spectral properties of the associated monodromy operator, showing in particular that it is a so-called Ritt operator under a natural ‘resonance’ condition. This allows us to deduce from our general result a precise description of the asymptotic behaviour of the corresponding solutions. In particular, we present conditions for rational rates of convergence to periodic solutions in the case where the convergence fails to be uniformly exponential. We illustrate our general results by applying them to concrete problems including the one-dimensional wave equation with periodic damping.

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