1,354 research outputs found
Averaging of equations of viscoelasticity with singularly oscillating external forces
Given , we consider for the nonautonomous
viscoelastic equation with a singularly oscillating external force together with the
{\it averaged} equation Under suitable assumptions on
the nonlinearity and on the external force, the related solution processes
acting on the natural weak energy space
are shown to possess uniform attractors . Within the
further assumption , the family turns out to
be bounded in , uniformly with respect to .
The convergence of the attractors to the attractor
of the averaged equation as is also
established
Asymptotic behaviour of random tridiagonal Markov chains in biological applications
Discrete-time discrete-state random Markov chains with a tridiagonal
generator are shown to have a random attractor consisting of singleton subsets,
essentially a random path, in the simplex of probability vectors. The proof
uses the Hilbert projection metric and the fact that the linear cocycle
generated by the Markov chain is a uniformly contractive mapping of the
positive cone into itself. The proof does not involve probabilistic properties
of the sample path and is thus equally valid in the nonautonomous deterministic
context of Markov chains with, say, periodically varying transitions
probabilities, in which case the attractor is a periodic path.Comment: 13 pages, 22 bibliography references, submitted to DCDS-B, added
references and minor correction
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