We study a class of nonlinear stochastic partial differential equations arising in themathematicalmodeling 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 separableHilbert 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.
International Journal of Stochastic Analysis
Hindawi Publishing Corporation
Article ID 868301
McKibben, M. A. (2013). Measure-Dependent Stochastic Nonlinear Beam Equations Driven by Fractional Brownian Motion. International Journal of Stochastic Analysis, Volume 2013(Article ID 868301), 1-16. http://dx.doi.org/http://dx.doi.org/10.1155/2013/868301