Measure-Dependent Stochastic Nonlinear Beam Equations Driven by Fractional Brownian Motion. (31st December 2013)

• Record Type: Journal Article
• Authors: McKibben, Mark A.
• Other Names: Tudor Ciprian A. Academic Editor.
• Is Part Of: International journal of stochastic analysis. Volume 2013(2013)
• Publication Date: 2013-12-31
• Subjects: Stochastic analysis -- Periodicals; Stochastic analysis; Periodicals; 519.22
• DOI: 10.1155/2013/868301
• Languages: English
• ISSNs: 2090-3332

Abstract

Abstract : 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.