Communications in Mathematical Analysis

Existence of Square-Mean Almost Periodic Solutions to Some Stochastic Hyperbolic Differential Equations with Infinite Delay

Paul H. Bezandry and Toka Diagana

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Abstract

In this paper, we make extensive use of the well-known Krasnoselskii fixed point theorem to obtain the existence of square-mean almost periodic solutions to some classes of hyperbolic stochastic evolution equations with infinite delay. Next, the existence of square-mean almost periodic solutions to not only the heat equation but also to a boundary value problem with infinite delay arising in control systems are studied.

Article information

Source
Commun. Math. Anal. Volume 8, Number 2 (2010), 103-124.

Dates
First available: 21 April 2010

Permanent link to this document
http://projecteuclid.org/euclid.cma/1271890671

Mathematical Reviews number (MathSciNet)
MR2576914

Zentralblatt MATH identifier
05707213

Subjects
Primary: 34K50: Stochastic functional-differential equations [See also , 60Hxx] 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 43A60: Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions 34B05: Linear boundary value problems 34C27: Almost and pseudo-almost periodic solutions 42A75: Classical almost periodic functions, mean periodic functions [See also 43A60] 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 35L90: Abstract hyperbolic equations

Keywords
Stochastic differential equation stochastic processes square-mean almost periodicity sectorial operator hyperbolic semigroup infinite delay Brownian motion

Citation

Bezandry, Paul H.; Diagana, Toka. Existence of Square-Mean Almost Periodic Solutions to Some Stochastic Hyperbolic Differential Equations with Infinite Delay. Communications in Mathematical Analysis 8 (2010), no. 2, 103--124. http://projecteuclid.org/euclid.cma/1271890671.


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