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On uniform attractors of explicit approximations

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Abstract

We prove a theorem stating that the uniform attractors of a family of semiprocesses that do not necessarily have a common time semigroup depend on the parameter uppersemicontinuously. We consider an explicit finite-difference scheme for a nonautonomous system of ordinary differential equations and an explicit spectral-difference scheme for the vorticity equation with time-dependent bounded right-hand side on a sphere. We obtain theorems on the existence of uniform attractors of numerical schemes and their closeness to true attractors of the original differential problems.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, Moscow, Russia

    V. M. Ipatova

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  1. V. M. Ipatova
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Original Russian Text © V.M. Ipatova, 2011, published in Differentsial’nye Uravneniya, 2011, Vol. 47, No. 4, pp. 574–583.

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Ipatova, V.M. On uniform attractors of explicit approximations. Diff Equat 47, 571–580 (2011). https://doi.org/10.1134/S0012266111040112

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  • DOI: https://doi.org/10.1134/S0012266111040112

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