Abstract:
The classical homogenization method of elliptic boundary value problems is based on the continuation of a solution, given in a perforated domain, to the entire initial domain. This method requires substantial restrictions on the perforated domain (the “strong connectedness” condition). In this paper we propose a new approach, which does not use the continuation technique. Here the “strong connectedness” is replaced by the usual connectedness.
Citation:
V. V. Zhikov, M. E. Rychago, “Homogenization of non-linear second-order elliptic equations in perforated domains”, Izv. Math., 61:1 (1997), 69–88
This publication is cited in the following 11 articles:
D. I. Borisov, “Asymptotic Analysis of Boundary-Value Problems for the Laplace Operator with Frequently Alternating Type of Boundary Conditions”, J Math Sci, 277:6 (2023), 841
D. I. Borisov, “Asimptoticheskii analiz kraevykh zadach dlya operatora Laplasa s chastoi smenoi tipa granichnykh uslovii”, Differentsialnye uravneniya s chastnymi proizvodnymi, SMFN, 67, no. 1, Rossiiskii universitet druzhby narodov, M., 2021, 14–129
Wang L., Xu Q., Zhao P., “Convergence Rates For Linear Elasticity Systems on Perforated Domains”, Calc. Var. Partial Differ. Equ., 60:2 (2021), 74
Giunti A., “Convergence Rates For the Homogenization of the Poisson Problem in Randomly Perforated Domains”, Netw. Heterog. Media, 16:3 (2021), 341–375
T. A. Mel'nik, O. A. Sivak, “Asymptotic analysis of a parabolic semilinear problem with nonlinear boundary multiphase interactions in a perforated domain”, J Math Sci, 164:3 (2010), 427
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G. V. Sandrakov, “Homogenization of variational inequalities for non-linear diffusion problems in perforated domains”, Izv. Math., 69:5 (2005), 1035–1059
V. V. Zhikov, M. E. Rychago, S. B. Shul'ga, “Homogenization of Monotone Operators by the Method of Two-Scale Convergence”, J Math Sci, 127:5 (2005), 2159
S. E. Pastukhova, “Homogenization of a mixed problem with Signorini condition for an elliptic operator in a perforated domain”, Sb. Math., 192:2 (2001), 245–260
S. E. Pastukhova, “On homogenization of a variational inequality for an elastic body with periodically distributed fissures”, Sb. Math., 191:2 (2000), 291–306
A. M. Shirokov, N. A. Smirnova, Yu. F. Smirnov, O. Castaños, A. Frank, “IBM: Discrete symmetry viewpoint”, Phys. Atom. Nuclei, 63:4 (2000), 695
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