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Homogenization problem in domain perforated by thin tubes with nonlinear robin type boundary condition

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References

  1. M. Bellieud and G. Bouchitté, Ann. Scuola Norm. Super. Pisa Cl. Sci. Ser. 4 26, 407–436 (1998).

    MATH  Google Scholar 

  2. A. Brillard and E. Pérez, in These d’Etat de A. Brillard (Montpellier, Francia, 1990), pp. 77–101.

    Google Scholar 

  3. D. Cioranescu, P. Donato, and R. Zaki, Asymptot. Anal. 53, 209–235 (2007).

    MathSciNet  MATH  Google Scholar 

  4. C. Conca, J. I. Díaz, A. Liãńn, and C. Timofte, J. Differ. Equations 40, 1–22 (2004).

    Article  Google Scholar 

  5. C. Conca, J. Planchard, and M. Vanninathan, Fluids and Periodic Structures (Wiley, Chichester, 1995).

    MATH  Google Scholar 

  6. D. Cioranescu and F. Murat, Res. Notes Math. 60, 98–138 (1982); 70, 154–178 (1982).

    MathSciNet  Google Scholar 

  7. A. Damlamian and Li. Ta-Tsien, J. Math. Pures Appl. 66, 351–361 (1987).

    MathSciNet  MATH  Google Scholar 

  8. D. Gómez, M. E. Pérez, and T. A. Shaposhnikova, “On Homogenization of Nonlinear Robin Type Boundary Conditions for Cavities along Manifolds and Associated Spectral Problems” (submitted to referee).

  9. M. Goncharenko, Proceedings of the International Conference on Homogenization and Applications to Material Sciences, Nice, France, June 6–10, 1995 GAKUTO Int. Ser. Math. Sci. Appl. Tokyo 9, 203–213 (1995).

    MathSciNet  Google Scholar 

  10. A. A. Kolpakov and A. G. Kolpakov, Capacity and Transport in Contrast Composite Structures: Asymptotic Analysis and Applications (CRC, Boca Raton, FL, 2010).

    Google Scholar 

  11. M. Lobo, O. A. Oleinik, M. E. Pérez, and T. A. Shaposhnikova, Ann. Scuola Norm. Super. Pisa Cl. Sci. Ser. 4 25, 611–629 (1997).

    MATH  Google Scholar 

  12. M. Lobo, M. E. Péres, V. V. Sukharev, and T. A. Shaposhnikova, Dokl. Math. 83, 34–38 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  13. V. A. Marchenko and E. Ya. Khruslov, Homogenized Models of Microinhomogeneous Media (Naukova Dumka, Kiev, 2005) [in Russian].

    Google Scholar 

  14. O. A. Oleinik, A. S. Shamaev, and G. A. Yosifian, Mathematical Problems in Elasticity and Homogenization (Mosk. Gos. Univ., Moscow, 1990; North-Holland, Amsterdam, 1992).

    Google Scholar 

  15. M. N. Zubova and T. A. Shaposhnikova, Differ. Equations 47, 78–90 (2011).

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Departamento de Matemáticas, Estadística y Computatíon, Universidad de Cantabria, 39005, Santander, Spain

    D. Gómez & M. Lobo

  2. Departamento de Matemática Aplicada y Ciencias de la Computatíon, Universidad de Cantabria, 39005, Santander, Spain

    M. E. Perez

  3. Department of Differential Equations, Moscow State University, Moscow, 119992, Russia

    T. A. Shaposhnikova & M. N. Zubova

Authors
  1. D. Gómez
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  2. M. Lobo
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  3. M. E. Perez
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  4. T. A. Shaposhnikova
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  5. M. N. Zubova
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Additional information

Original Russian Text © D. Gómez, M. Lobo, M.E. Perez, T.A. Shaposhnikova, M.N. Zubova, 2013, published in Doklady Akademii Nauk, 2013, Vol. 448, No. 1, pp. 11–18.

The article was translated by the authors.

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Gómez, D., Lobo, M., Perez, M.E. et al. Homogenization problem in domain perforated by thin tubes with nonlinear robin type boundary condition. Dokl. Math. 87, 5–11 (2013). https://doi.org/10.1134/S106456241301002X

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  • DOI: https://doi.org/10.1134/S106456241301002X

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