Abstract functional second-order stochastic evolution equations with applications

Thumbnail
Permanent Link
http://hdl.handle.net/11603/4375
Collections
Metadata
Show full item record
Author/Creator
Date
2017-01-24
Type of Work
Text
journal articles
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.
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.