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Homogenization of Random Nonstationary Convection-Diffusion Problem

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Book cover Multiscale Problems in Science and Technology

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Abstract

We deal with nonstationary convection-diffusion problem in a medium with a periodic microstructure whose characteristics are stationary ergodic rapidly oscillating in time random functions. Under the assumption that the coefficients of the corresponding parabolic equation possess certain mixing properties, we show that, in appropriate moving coordinates, the law of the solutions of the original problem converges weakly in the energy functional space to a solution of a stochastic partial differential equation. This limit stochastic PDE is well-posed and thus the limit measure is uniquely defined.

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References

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Author information

Authors and Affiliations

  1. Institute for Information Transmission Problems, 19, Bol’shoi Karetnii, Moscow, 101447, Russia

    Marina Kleptsyna

  2. Department of Mathematics, Narvik Institute of Technology, HiN, Postbox 385, 8505, Narvik, Norway

    Andrey Piatnitski

  3. P.N.Lebedev Physical Institute RAS, Leninski prospect 53, Moscow, 117924, Russia

    Andrey Piatnitski

Authors
  1. Marina Kleptsyna
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  2. Andrey Piatnitski
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000, Zagreb, Croatia

    Nenad Antonić

  2. Dept. of Applied Analysis and Scientific Computing, CWI Amsterdam, P.O.Box 94079, Kruislaan 413, 1090 GB, Amsterdam, The Netherlands

    C. J. van Duijn

  3. IWR, University of Heidelberg, Im Neuenheimer Feld 368, 69120, Heidelberg, Germany

    Willi Jäger

  4. Analyse Numérique, Bât 101 U.F.R. Mathématiques, Université Lyon 1, 43, Bd. du 11 Novembre 1918, 69622, Villeurbanne Cedex, France

    Andro Mikelić

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© 2002 Springer-Verlag Berlin Heidelberg

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Kleptsyna, M., Piatnitski, A. (2002). Homogenization of Random Nonstationary Convection-Diffusion Problem. In: Antonić, N., van Duijn, C.J., Jäger, W., Mikelić, A. (eds) Multiscale Problems in Science and Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56200-6_11

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  • DOI: https://doi.org/10.1007/978-3-642-56200-6_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43584-6

  • Online ISBN: 978-3-642-56200-6

  • eBook Packages: Springer Book Archive

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