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Pullback Attractors in Dissipative Nonautonomous Differential Equations Under Discretization

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Abstract

The effects of discretization on the nonautonomous pullback attractors of skew-product flows generated by a class of dissipative differential equations, are investigated, It is assumed that the vector, field of the differential equations varies in time due to the input of an autonomous dynamical system acting on a compact metric space. In particular, it is shown that the corresponding discrete time skew-product system generated by a one-step numerical scheme with variable timesteps also has a pullback attractor, the component subsets of which converge upper semicontinuously to their counterparts of the pullback attractor of the original continuous time system.

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Authors and Affiliations

  1. Faculty of Mathematics and Informatics, State University of Moldova, Mateevich str. 60, Kishinev, Moldova, 2009

    D. N. Cheban

  2. FB Mathematik, Johann Wolfgang Goethe Universität, D-60054, Frankfurt am Main, Germany

    P. E. Kloeden

  3. FB Angewandte Naturwissenschaften, Fachhochschule Merseburg, D-06217, Merseburg, Germany

    B. Schmalfuß

Authors
  1. D. N. Cheban
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  2. P. E. Kloeden
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  3. B. Schmalfuß
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Cheban, D.N., Kloeden, P.E. & Schmalfuß, B. Pullback Attractors in Dissipative Nonautonomous Differential Equations Under Discretization. Journal of Dynamics and Differential Equations 13, 185–213 (2001). https://doi.org/10.1023/A:1009000700546

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