Skip to main content
Article
Measure-Dependent Stochastic Nonlinear Beam Equations Driven by Fractional Brownian Motion
International Journal of Stochastic Analysis
  • Mark A. McKibben, West Chester University of Pennsylvania
Document Type
Article
Publication Date
1-1-2013
Abstract
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.
Publisher
Hindawi Publishing Corporation
DOI
http://dx.doi.org/10.1155/2013/868301
Citation Information
Mark A. McKibben. "Measure-Dependent Stochastic Nonlinear Beam Equations Driven by Fractional Brownian Motion" International Journal of Stochastic Analysis Vol. Volume 2013 Iss. Article ID 868301 (2013) p. 1 - 16
Available at: http://works.bepress.com/mark_mckibben/1/