Asymptotic Behaviour of Coupled Systems in Discrete and Continuous Time

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Asymptotic Behaviour of Coupled Systems in Discrete and Continuous Time. / Paunonen, Lassi; Seifert, David.

julkaisussa: JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, Vuosikerta 30, Nro 2, 06.2018, s. 433-445.

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Paunonen, Lassi ; Seifert, David. / Asymptotic Behaviour of Coupled Systems in Discrete and Continuous Time. Julkaisussa: JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS. 2018 ; Vuosikerta 30, Nro 2. Sivut 433-445.

Bibtex - Lataa

@article{1a312ea3e262469f9550e28dd6385c91,

title = "Asymptotic Behaviour of Coupled Systems in Discrete and Continuous Time",

abstract = "This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for initial values satisfying a slightly stronger condition we obtain an optimal estimate on the rate of convergence. By establishing a connection with a related problem in continuous time, we are able to use this optimal estimate to improve the rate of convergence in the continuous setting obtained by the authors in a previous paper. We illustrate the power of the general approach by using it to study several concrete examples, both in continuous and in discrete time.",

keywords = "$C_0$-semigroups, Asymptotic behaviour, Power-boundeness, Rates of convergence, Recurrence relations, Spectral theory, System",

author = "Lassi Paunonen and David Seifert",

year = "2018",

month = "6",

doi = "10.1007/s10884-016-9547-1",

language = "English",

volume = "30",

pages = "433--445",

journal = "JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS",

issn = "1040-7294",

publisher = "Springer Verlag",

number = "2",

}

RIS (suitable for import to EndNote) - Lataa

TY - JOUR

T1 - Asymptotic Behaviour of Coupled Systems in Discrete and Continuous Time

AU - Paunonen, Lassi

AU - Seifert, David

PY - 2018/6

Y1 - 2018/6

N2 - This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for initial values satisfying a slightly stronger condition we obtain an optimal estimate on the rate of convergence. By establishing a connection with a related problem in continuous time, we are able to use this optimal estimate to improve the rate of convergence in the continuous setting obtained by the authors in a previous paper. We illustrate the power of the general approach by using it to study several concrete examples, both in continuous and in discrete time.

AB - This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for initial values satisfying a slightly stronger condition we obtain an optimal estimate on the rate of convergence. By establishing a connection with a related problem in continuous time, we are able to use this optimal estimate to improve the rate of convergence in the continuous setting obtained by the authors in a previous paper. We illustrate the power of the general approach by using it to study several concrete examples, both in continuous and in discrete time.

KW - $C_0$-semigroups

KW - Asymptotic behaviour

KW - Power-boundeness

KW - Rates of convergence

KW - Recurrence relations

KW - Spectral theory

KW - System

U2 - 10.1007/s10884-016-9547-1

DO - 10.1007/s10884-016-9547-1

M3 - Article

VL - 30

SP - 433

EP - 445

JO - JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS

JF - JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS

SN - 1040-7294

IS - 2

ER -

TUTCRIS