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# On the mean ergodicity of weak solutions of an abstract evolution equation

### Abstract

Found are conditions of rather general nature sufficient for the existence of the limit at infinity of the Cesàro means $$\frac{1}{t} \int_0^ty(s)\,ds$$ for every bounded weak solution $y(\cdot)$ of the abstract evolution equation $$y'(t)=Ay(t),\ t\ge 0,$$ with a closed linear operator $A$ in a Banach space $X$.

Key words: Mean ergodicity, weak solution.

### Article Information

 Title On the mean ergodicity of weak solutions of an abstract evolution equation Source Methods Funct. Anal. Topology, Vol. 24 (2018), no. 1, 53-70 MathSciNet MR3783818 Milestones Received 10/03/2017; Revised 03/09/2017 Copyright The Author(s) 2018 (CC BY-SA)

### Authors Information

Marat V. Markin
Department of Mathematics, California State University, Fresno, 5245 N. Backer Avenue, M/S PB 108, Fresno, CA 93740-8001, USA

### Citation Example

Marat V. Markin, On the mean ergodicity of weak solutions of an abstract evolution equation, Methods Funct. Anal. Topology 24 (2018), no. 1, 53-70.

### BibTex

@article {MFAT1025,
AUTHOR = {Marat V. Markin},
TITLE = {On the mean ergodicity of weak solutions of an abstract evolution equation},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {24},
YEAR = {2018},
NUMBER = {1},
PAGES = {53-70},
ISSN = {1029-3531},
MRNUMBER = {MR3783818},
URL = {http://mfat.imath.kiev.ua/article/?id=1025},
}

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