Robin's nonlinear problem in domains with a fine-grained random boundary

Authors

  • E.Ya. Khruslov B.I. Verkin Institute for Low Temperature Physics and Engineering of the NAS of Ukraine, Kharkiv
  • L.A. Khilkova Institute of Chemical Technologies of the Volodymyr Dahl East Ukrainian National University, Rubizhne

DOI:

https://doi.org/10.15407/dopovidi2017.09.003

Keywords:

Homogenization, random distribution, Robin's boundary condition, stationary diffusion

Abstract

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References

Marchenko, V. A. & Khruslov, E. Ya. (1974). Boundary-value problems in domains with a fine-grained boundary. Kiev: Naukova Dumka (in Russian).

Shiryaev, A. N. (2004). Probability-1. Moscow: MTsNMO (in Russian).

Bogolyubov, N. N. (1970). Selected works. Vol. 2. Kiev: Naukova Dumka (in Russian).

Gikhman, I. I., Skorokhod, A. V. & Yadrenko, M. I. (1973). Theory of Probability and Mathematical Statistics. Kiev: Vyshcha shkola (in Russian).

Berlyand, L. V. & Khruslov, E. Ya., (2005). Ginzburg—Landau model of a liquid crystal with random inclusions. J. Math. Phys., 46, 095107, 15 p. https://doi.org/10.1063/1.2013127

Marchenko, V. A. & Khruslov, E. Ya. (2005). Homogenized models of micro-inhomogeneous media. Kiev: Naukova Dumka (in Russian).

Khilkova, L. O. (2016). Homogenization of the diffusion equation in domains with the fine-grained boundary with the nonlinear boundary Robin condition. Visnyk of V. N. Karazin Kharkiv National University. Ser. Math., Appl. Math. and Mech., 84, rp. 93-111 (in Russian).

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Published

17.09.2024

How to Cite

Khruslov, E., & Khilkova, L. (2024). Robin’s nonlinear problem in domains with a fine-grained random boundary . Reports of the National Academy of Sciences of Ukraine, (9), 3–8. https://doi.org/10.15407/dopovidi2017.09.003

Issue

No. 9 (2017): Reports of the National Academy of Sciences of Ukraine

Section

Mathematics

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