Random attractor for stochastic partial functional differential equations with infinite delay

Honglian You; Rong Yuan

doi:10.4134/BKMS.2014.51.5.1469

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2014; 51(5): 1469-1484

Printed September 30, 2014

https://doi.org/10.4134/BKMS.2014.51.5.1469

Random attractor for stochastic partial functional differential equations with infinite delay

Honglian You and Rong Yuan

Binzhou University, Beijing Normal University

Abstract

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Abstract

In this paper we are concerned with a class of stochastic partial functional differential equations with infinite delay. Supposing that the linear part is a Hille-Yosida operator but not necessarily densely defined and employing the integrated semigroup and random dynamics theory, we present some appropriate conditions to guarantee the existence of a random attractor.

Keywords: random attractor, Hille-Yosida, tempered, infinite delay

MSC numbers: 34D45, 47D62, 35R60