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Asymptotics for periodic systems

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Asymptotics for periodic systems. / Paunonen, Lassi; Seifert, David.

julkaisussa: Journal of Differential Equations, Vuosikerta 266, Nro 11, 05.2019, s. 7152-7172.

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Harvard

Paunonen, L & Seifert, D 2019, 'Asymptotics for periodic systems', Journal of Differential Equations, Vuosikerta. 266, Nro 11, Sivut 7152-7172. https://doi.org/10.1016/j.jde.2018.11.028

APA

Paunonen, L., & Seifert, D. (2019). Asymptotics for periodic systems. Journal of Differential Equations, 266(11), 7152-7172. https://doi.org/10.1016/j.jde.2018.11.028

Vancouver

Paunonen L, Seifert D. Asymptotics for periodic systems. Journal of Differential Equations. 2019 touko;266(11):7152-7172. https://doi.org/10.1016/j.jde.2018.11.028

Author

Paunonen, Lassi ; Seifert, David. / Asymptotics for periodic systems. Julkaisussa: Journal of Differential Equations. 2019 ; Vuosikerta 266, Nro 11. Sivut 7152-7172.

Bibtex - Lataa

@article{5a51a89709184a2ea5674a77fc0a0dbb,
title = "Asymptotics for periodic systems",
abstract = "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.",
keywords = "Damped wave equation, Evolution family, Non-autonomous system, Periodic, Rates of convergence, Ritt operator",
author = "Lassi Paunonen and David Seifert",
year = "2019",
month = "5",
doi = "10.1016/j.jde.2018.11.028",
language = "English",
volume = "266",
pages = "7152--7172",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "Elsevier",
number = "11",

}

RIS (suitable for import to EndNote) - Lataa

TY - JOUR

T1 - Asymptotics for periodic systems

AU - Paunonen, Lassi

AU - Seifert, David

PY - 2019/5

Y1 - 2019/5

N2 - 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.

AB - 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.

KW - Damped wave equation

KW - Evolution family

KW - Non-autonomous system

KW - Periodic

KW - Rates of convergence

KW - Ritt operator

U2 - 10.1016/j.jde.2018.11.028

DO - 10.1016/j.jde.2018.11.028

M3 - Article

VL - 266

SP - 7152

EP - 7172

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 11

ER -