Homogenization of boundary value problems in perforated domains with the third boundary condition and the resulting change in the character of the nonlinearity in the problem

Author:

Zubova M. N.,Shaposhnikova T. A.

Publisher

Pleiades Publishing Ltd

Subject

General Mathematics,Analysis

Reference10 articles.

1. Goncharenko, M., The Asymptotic Behaviour of the Third Boundary Value Problem Solutions in Domains with Fine-Grained Boundaries, GAKUTO Internat. Ser. Math. Sci. Appl., 1997, vol. 9, pp. 203–213.

2. Oleinik, O.A. and Shaposhnikova, T.A., On a Homogenization Problem with a Small Parameter in a Partially Punctured Domain with a Boundary Condition of Mixed Type on the Boundary of the Holes, Differ. Uravn., 1995, vol. 31, no. 7, pp. 1140–1150.

3. Oleinik, O.A. and Shaposhnikova, T.A., On the Homogenization of the Poisson Equation in Partially Perforated Domains with Arbitrary Density of Cavities and Mixed Type Conditions on Their Boundary, Rend. Mat. Acc. Lincei., 1996, ser. 9, vol. 7, pp. 129–146.

4. Belyaev, A.G., Pyatnitskii, A.L., and Chechkin, G.A., Averaging in a Perforated Domain with an Oscillating Third Boundary Condition, Mat. Sb., 2001, vol. 193, no. 7, pp. 3–20.

5. Eger, V., Oleinik, O.A., and Shamaev, A.S., On the Asymptotic Behavior of Solutions of a Boundary Value Problem for the Laplace Equation in a Partially Punctured Domain with Boundary Conditions of the Third Kind on the Boundaries of Cavities, Tr. Mosk. Mat. Obs., 1997, vol. 58, pp. 187–223.

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