Abstract functional second-order stochastic evolution equations with applications

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Permanent Link

http://hdl.handle.net/11603/4375

Collections

Goucher College Faculty and Staff Collection

Author/Creator

Author/Creator ORCID

Date

2017-01-24

Type of Work

journal articles
Text

Department

Mathematics

Program

Center for Data, Mathematical, and Computational Sciences

Citation of Original Publication

M. McKibben, M.Webster, “Abstract functional second-order stochastic evolution equations with applications, ” Afrika Matematika, (2017), 1-26, doi: 10.1007/s13370-017-0480-1.

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Subjects

Cosine family
Second-order equation
Fractional Brownian motion
Stochastic evolution equation

Abstract

We investigate a class of abstract second-order damped functional stochastic evolution equations driven by a fractional Brownian motion in a separable Hilbert space. The global existence of mild solutions is established under various growth and compactness conditions. The case of a nonlocal initial condition is addressed. A related convergence result is discussed, and the theory is applied to stochastic wave and beam equations, as well as a spring-mass system, for illustrative purposes.