International Journal of Stochastic Analysis
Volume 2013 (2013), Article ID 868301, 16 pages
Research Article

Measure-Dependent Stochastic Nonlinear Beam Equations Driven by Fractional Brownian Motion

Department of Mathematics, West Chester University of Pennsylvania, 25 University Avenue, West Chester, PA 19343, USA

Received 1 October 2013; Accepted 9 November 2013

Academic Editor: Ciprian A. Tudor

Copyright © 2013 Mark A. McKibben. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study a class of nonlinear stochastic partial differential equations arising in the mathematical modeling of the transverse motion of an extensible beam in the plane. Nonlinear forcing terms of functional-type and those dependent upon a family of probability measures are incorporated into the initial-boundary value problem (IBVP), and noise is incorporated into the mathematical description of the phenomenon via a fractional Brownian motion process. The IBVP is subsequently reformulated as an abstract second-order stochastic evolution equation driven by a fractional Brownian motion (fBm) dependent upon a family of probability measures in a real separable Hilbert space and is studied using the tools of cosine function theory, stochastic analysis, and fixed-point theory. Global existence and uniqueness results for mild solutions, continuous dependence estimates, and various approximation results are established and applied in the context of the model.