Abstract functional second-order stochastic evolution equations with applications
Date
2017-01-24Type of Work
Textjournal articles
Department
MathematicsProgram
Center for Data, Mathematical, and Computational SciencesCitation 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 familySecond-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.