Controllability of semilinear stochastic evolution equations in Hilbert space

P. Balasubramaniam,J. P. Dauer

doi:10.1155/s1048953301000296

Abstract

Controllability of semilinear stochastic evolution equations is studied by using stochastic versions of the well-known fixed point theorem and semigroup theory. An application to a stochastic partial differential equation is given.

Highlights

Among the methods employed for the controllability of nonlinear systems in finite and infinite dimensional Banach spaces, fixed point techniques are widely used
Several authors have extended the classical finite dimensional controllability results to infinite dimensional controllability results represented by the evolution equations with bounded and unbounded operators in Banach spaces using semigroup theorem
The semigroup theory gives a unified treatment of a wide class of stochastic parabolic, hyperbolic and functional differential equations, and much effort has been devoted to the study of the controllability results of such evolution equations

Summary

Introduction

Among the methods employed for the controllability of nonlinear systems in finite and infinite dimensional Banach spaces, fixed point techniques are widely used. A stochastic model for drug distribution in a closed biological system with a simplified heart, one organ or capillary bed, and recirculation of the blood with a constant rate of flow, where the heart is considered as a mixing chamber of constant volume was described in [21]. K(s,x(s; co); co) C/V){x(s; co) .1(1, s r; co)}, and Xl(1 s; co) 0 if s < 0, where C is the constant volume flow rate of plasma in the capillary bed and zl(1,s; co) is the drug concentration in the plasma leaving the organ at time s. The main objective of this paper is to derive the controllability conditions of semilinear stochastic evolution equations (1.1) in Hilbert space having the probability measure #(t). The considered system is an abstract formulation of stochastic partial differential equations (see [12])

Preliminaries

B I 2 c4 and I w-ill 2 65

Main Result

Example