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.

Full Text

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
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},
       URL = {http://mfat.imath.kiev.ua/article/?id=1025},
}

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