On the stability of stationary solutions of stochastic evolutions equations with delays
by
María J. Garrido-Atienza
University of Seville (Spain)
Coauthors: Tomás Caraballo (University of Seville, Spain), Björn Schmalfuss (University of Merseburg, Germany)

The aim of this work is to prove some sufficient conditions ensuring existence, uniqueness and exponential stability of nontrivial stationary solutions for a class of delay stochastic partial differential equations.

In particular, we consider delay stochastic differential equations where the main operator generates a strongly continuous contraction semigroup, the delay will appear by means of a family of nonlinear Lipschitz continuous operators, and we will consider a linear multiplicative noise. The zero will not be a solution for these equations.

We will prove the existence of random fixed points which generate stationary solutions that will be exponentially attracting in the L² sense and almost surely.

Date received: May 29, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # calo-24.