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Fast and Slow Boundary Oscillations in a Thin Domain

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Advances in Differential Equations and Applications

Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 4))

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Abstract

In this work we analyze the behavior of the solutions of the Laplace operator with Neumann boundary conditions in a 2-dimensional thin domain with order of thickness ε which presents a high oscillatory behavior at the top and a weak oscillatory behavior at the bottom boundary. We obtain the asymptotic homogenized problem as ε → 0 and we are interested in understanding how the extremely different order of the oscillations affects to the limit.

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Acknowledgements

Both authors are partially supported by grant MTM2012-31298, MINECO, Spain and Grupo de Investigación CADEDIF, UCM. The second author, Manuel Villanueva-Pesqueira, also partially supported by a FPU fellowship (AP2010-0786) from the Government of Spain.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040, Madrid, Spain

    José M. Arrieta & Manuel Villanueva-Pesqueira

  2. Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, 28049, Madrid, Spain

    José M. Arrieta & Manuel Villanueva-Pesqueira

Authors
  1. José M. Arrieta
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  2. Manuel Villanueva-Pesqueira
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Corresponding author

Correspondence to José M. Arrieta .

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Editors and Affiliations

  1. Dept. de Mathemàtiques and IMAC, Universitat Jaume I, Castelló, Spain

    Fernando Casas

  2. Dept. de Mathemàtiques and IMAC, Universitat Jaume I, Castelló, Spain

    Vicente Martínez

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Arrieta, J.M., Villanueva-Pesqueira, M. (2014). Fast and Slow Boundary Oscillations in a Thin Domain. In: Casas, F., Martínez, V. (eds) Advances in Differential Equations and Applications. SEMA SIMAI Springer Series, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-06953-1_2

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