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Boundary homogenization in domains with randomly oscillating boundary

Author

Listed:
  • Amirat, Youcef
  • Bodart, Olivier
  • Chechkin, Gregory A.
  • Piatnitski, Andrey L.

Abstract

We consider a model homogenization problem for the Poisson equation in a domain with a rapidly oscillating boundary which is a small random perturbation of a fixed hypersurface. A Fourier boundary condition with random coefficients is imposed on the oscillating boundary. We derive the effective boundary condition, prove a convergence result, and establish error estimates.

Suggested Citation

  • Amirat, Youcef & Bodart, Olivier & Chechkin, Gregory A. & Piatnitski, Andrey L., 2011. "Boundary homogenization in domains with randomly oscillating boundary," Stochastic Processes and their Applications, Elsevier, vol. 121(1), pages 1-23, January.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:1:p:1-23
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    References listed on IDEAS

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    1. Campillo, Fabien & Kleptsyna, Marina & Piatnitski, Andrey, 2001. "Homogenization of random parabolic operator with large potential," Stochastic Processes and their Applications, Elsevier, vol. 93(1), pages 57-85, May.
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    Cited by:

    1. El Jarroudi, Mustapha, 2019. "A mathematical model for turbulent transport through thin randomly oscillating layers surrounding a fixed domain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 178-195.

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