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Homogenization of Liouville Equations Beyond a Stationary Ergodic Setting

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Abstract

We consider the homogenization problem of the Liouville equation for non-crystalline materials namely, the coefficients are given by the composition of stationary functions with stochastic deformations. We show the asymptotic equations, which involves both macroscopic and microscopic scales.

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Authors and Affiliations

  1. Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil

    Taynara Andrade & Wladimir Neves

  2. Universidade Federal de Minas Gerais, Minas Gerais, Brazil

    Jean Silva

Authors
  1. Taynara Andrade
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  2. Wladimir Neves
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  3. Jean Silva
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Corresponding author

Correspondence to Wladimir Neves.

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Conflict of interest

Author Wladimir Neves has received research grants from CNPq through the Grant 308064/2019-4. Author Jean Silva has received research grants from CNPQ through the Grant 302331/2017-4.

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Communicated by C. Le Bris.

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Andrade, T., Neves, W. & Silva, J. Homogenization of Liouville Equations Beyond a Stationary Ergodic Setting. Arch Rational Mech Anal 237, 999–1040 (2020). https://doi.org/10.1007/s00205-020-01524-4

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  • DOI: https://doi.org/10.1007/s00205-020-01524-4

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