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

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  • Mark A. McKibben

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.

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  • Mark A. McKibben, 2013. "Measure-Dependent Stochastic Nonlinear Beam Equations Driven by Fractional Brownian Motion," International Journal of Stochastic Analysis, Hindawi, vol. 2013, pages 1-16, December.
    • Handle: RePEc:hin:jnijsa:868301
    DOI: 10.1155/2013/868301
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