Asymptotic Behaviour of Coupled Systems in Discrete and Continuous Time
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Details
| Original language | English |
|---|---|
| Pages (from-to) | 433-445 |
| Number of pages | 13 |
| Journal | JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS |
| Volume | 30 |
| Issue number | 2 |
| Early online date | 22 Aug 2016 |
| DOIs | |
| Publication status | Published - Jun 2018 |
| Publication type | A1 Journal article-refereed |
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.
ASJC Scopus subject areas
Keywords
- $C_0$-semigroups, Asymptotic behaviour, Power-boundeness, Rates of convergence, Recurrence relations, Spectral theory, System