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ATTRACTORS FOR A LATTICE DYNAMICAL SYSTEM GENERATED BY NON-NEWTONIAN FLUIDS MODELING SUSPENSIONS

Universidad Miguel Hernández, Centro de Investigación Operativa, Avda. Universidad s/n, 03202 Elche (Alicante), Spain

Universitat de València, Departament d'Economia Aplicada, Facultat d'Economia, Campus dels Tarongers s/n, 46022 València, Spain

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JOSÉ VALERO

Universidad Miguel Hernández, Centro de Investigación Operativa, Avda. Universidad s/n, 03202 Elche (Alicante), Spain

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https://doi.org/10.1142/S0218127410027295Cited by:11 (Source: Crossref)

Abstract

In this paper we consider a lattice dynamical system generated by a parabolic equation modeling suspension flows. We prove the existence of a global compact connected attractor for this system and the upper semicontinuity of this attractor with respect to finite-dimensional approximations. Also, we obtain a sequence of approximating discrete dynamical systems by the implementation of the implicit Euler method, proving the existence and the upper semicontinuous convergence of their global attractors.

Dedicated to the memory of Valery S. Melnik

Keywords:

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