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Persistence of Periodic Orbits for Perturbed Dissipative Dynamical Systems Read chapter Read first chapter

2013 | OriginalPaper | Chapter

Anomalous Diffusion in Polymers: Long-Time Behaviour

Author : Dmitry A. Vorotnikov

Published in: Infinite Dimensional Dynamical Systems

Publisher: Springer New York

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Abstract

We study the Dirichlet boundary value problem for viscoelastic diffusion in polymers. We show that its weak solutions generate a dissipative semiflow. We construct the minimal trajectory attractor and the global attractor for this problem.

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previous chapter Bifurcation of Limit Cycles from a Non-Hamiltonian Quadratic Integrable System with Homoclinic Loop
next chapter Erratum to: Infinite Dimensional Dynamical Systems
Footnotes
1
Formula (4) describes the following peculiarities of the processes under consideration. The polymer network in the glassy state (low concentration area) is severely entangled, so β is approximately equal to some small βG. In the high concentration areas the system is in the rubbery state: the network disentangles, so the relaxation time is small, and its inverse is close to βR > βG. The glass-rubber phase transition occurs near a certain concentration uRG. However, we assume that β also depends on stress, cf. [2, 11, 26].
 
2
Trajectory attractors for problems with uniqueness were investigated in [6] only as an intermediate step on the way to usual global attractors of semigroups.
 
3
The case μ = 0 (“the Maxwell model” [9, 30]) is admissible as well.
 
4
e.g. in form (4).
 
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Metadata
Title
Anomalous Diffusion in Polymers: Long-Time Behaviour
Author
Dmitry A. Vorotnikov
Copyright Year
2013
Publisher
Springer New York
Book
Infinite Dimensional Dynamical Systems

Print ISBN: 978-1-4614-4522-7

Electronic ISBN: 978-1-4614-4523-4

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-1-4614-4523-4_19

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