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On the convergence of solutions and eigenelements of a boundary value problem in a domain perforated along the boundary

  • Partial Differential Equations
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Abstract

We consider a boundary value problem in a model domain periodically perforated along the boundary. We assume that the homogeneous Neumann condition is posed on the external boundary and the homogeneous Dirichlet condition is posed on the boundary of the cavities. A limit (homogenized) problem is obtained. We prove the convergence of the solutions, eigenvalues, and eigenfunctions of the original problem to the solutions, eigenvalues, and eigenfunctions, respectively, of the limit problem.

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Authors and Affiliations

  1. Bashkir State Pedagogical University, Ufa, Russia

    R. R. Gadyl’shin, Yu. O. Koroleva & G. A. Chechkin

  2. Moscow State University, Moscow, Russia

    R. R. Gadyl’shin, Yu. O. Koroleva & G. A. Chechkin

Authors
  1. R. R. Gadyl’shin
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  2. Yu. O. Koroleva
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  3. G. A. Chechkin
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Original Russian Text © R.R. Gadyl’shin, Yu.O. Koroleva, G.A. Chechkin, 2010, published in Differentsial’nye Uravneniya, 2010, vol. 46, no. 5, pp. 665–677.

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Gadyl’shin, R.R., Koroleva, Y.O. & Chechkin, G.A. On the convergence of solutions and eigenelements of a boundary value problem in a domain perforated along the boundary. Diff Equat 46, 667–680 (2010). https://doi.org/10.1134/S001226611005006X

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  • DOI: https://doi.org/10.1134/S001226611005006X

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