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Averaging of the Neumann problems for nonlinear elliptic equations in domains with accumulators

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Abstract

We study the asymptotic behavior of solutions of the Neumann problems for nonlinear elliptic equations in domains with accumulators, which simulate porous media. An effective description is given for an averaged problem, which, in the case of simple accumulators, is a problem for the system of a functional equation and a differential equation; in the case of double accumulators, it is a problem for the system of two functional equations and a differential equation.

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References

  1. E. Ya. Khruslov, “Asymptotic behavior of the solutions of the second boundary-value problem under the refinement of the domain boundary,”Mat. Sb.,106, No. 4, 604–621 (1978).

    Google Scholar 

  2. E. Ya. Khruslov, “On the convergence of solutions of the second boundary-value problem in weakly connected domains,” in:Theory of Operators in Functional Spaces and Its Applications [in Russian], Naukova Dumka, Kiev (1981).

    Google Scholar 

  3. E. Ya. Khruslov,Averaging Model of Nonstationary Diffusion in Porous Media [in Russian], Preprint No. 50-88, Physicotechnical Institute of Low Temperatures, Ukrainian Academy of Sciences, Kharkov (1988).

    Google Scholar 

  4. E. Ya. Khruslov, “Averaging models of diffusion in porous media,”Dokl. Akad. Nauk Ukr. SSR,309, No. 2, 332–335 (1989).

    Google Scholar 

  5. L. V. Berlyand and I. Yu. Chudinovich, “Averaging of boundary-value problems for differential operators of the higher orders in domains with cavities,”Dokl. Akad. Nauk Ukr. SSR,272, No. 4, 777–780 (1983).

    Google Scholar 

  6. A. A. Kovalevskii,Second Boundary-Value Problem for Variational Elliptic Equations in Domains with Complex Structure [in Russian], Preprint No. 84.40, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1984).

    Google Scholar 

  7. A. A. Kovalevskii,G-Convergence and Averaging of Nonlinear Elliptic Operators with Various Domains of Definition [in Russian], Preprint No. 90.01, Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk (1990).

    Google Scholar 

  8. L. S. Pankratov,On the Convergence of Solutions of Variational Problems in Weakly Connected Domains [in Russian], Preprint No. 53-88, Physicotechnical Institute of Low Temperatures, Ukrainian Academy of Sciences, Kharkov (1988).

    Google Scholar 

  9. A. A. Kovalevskii, “G-Convergence of abstract operators defined on weakly connected spaces,”Dokl. Akad. Nauk Ukr. SSR,9, 27–30 (1991).

    Google Scholar 

  10. L. S. Pankratov, “Asymptotic behavior of solutions of variational problems in domains with accumulators,”Teor. Funkts., Funkts. Anal. Prilozhen.,54, 97–105 (1990).

    Google Scholar 

  11. J.-L. Lions,Some Methods for Solving Nonlinear Boundary-Value Problems [Russian translation], Mir, Moscow (1972).

    Google Scholar 

  12. O. A. Ladyzhenskaya,Boundary-Value Problems in Mathematical Physics [in Russian], Nauka, Moscow (1973).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk

    A. A. Kovalevskii

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  1. A. A. Kovalevskii
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 2, pp. 194–212, February, 1995.

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Kovalevskii, A.A. Averaging of the Neumann problems for nonlinear elliptic equations in domains with accumulators. Ukr Math J 47, 227–249 (1995). https://doi.org/10.1007/BF01056714

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  • DOI: https://doi.org/10.1007/BF01056714

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