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Applicable Analysis
An International Journal
Volume 65, 1997 - Issue 3-4
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Original Articles

On some homogenization problems in perforated domains with nonlinear boundary conditions

G.A. Yosifian Russian Academy of Scienices, Institute for Problems in Mechanics,
Pages 257-288 | Received 01 Oct 1996, Published online: 02 May 2007

Citations (17)

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Read on this site (3)

D. Gómez, M. Lobo, M.E. Pérez & T.A. Shaposhnikova. (2013) Averaging of variational inequalities for the Laplacian with nonlinear restrictions along manifolds. Applicable Analysis 92:2, pages 218-237.
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G. Cardone, A. Corbo Esposito & S.A. Nazarov. (2009) Korn's inequality for periodic solids and convergence rate of homogenization. Applicable Analysis 88:6, pages 847-876.
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G. A. Yosifian. (1998) Some homogenization problems for the system of elasticity with nonlinear boundary conditions in perforated domains. Applicable Analysis 71:1-4, pages 379-411.
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Articles from other publishers (14)

Changqing Ye, Eric T. Chung & Jun-zhi Cui. (2023) Homogenization with the Quasistatic Tresca Friction Law: Qualitative and Quantitative Results. Chinese Annals of Mathematics, Series B 44:5, pages 781-802.
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Eric Chung, Jiuhua Hu & Sai-Mang Pun. (2021) Convergence of the CEM-GMsFEM for Stokes flows in heterogeneous perforated domains. Journal of Computational and Applied Mathematics 389, pages 113327.
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Changqing Ye, Junzhi Cui & Hao Dong. (2021) Asymptotic Analysis of Nonlinear Robin-Type Boundary Value Problems with Small Periodic Structure. Multiscale Modeling & Simulation 19:2, pages 830-845.
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L. Baffico. (2016) Two-scale homogenization of the Poisson equation with friction boundary condition in a perforated domain. Asymptotic Analysis 96:3-4, pages 331-349.
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Sebastian Fillep, Julia Orlik, Zoufine Bare & Paul Steinmann. (2013) Homogenization in periodically heterogeneous elastic bodies with multiple micro-contact. Mathematics and Mechanics of Solids 19:8, pages 1011-1021.
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Willi Jäger, Maria Neuss-Radu & Tatiana A. Shaposhnikova. (2014) Homogenization of a variational inequality for the Laplace operator with nonlinear restriction for the flux on the interior boundary of a perforated domain. Nonlinear Analysis: Real World Applications 15, pages 367-380.
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W. Jäger, M. Neuss-Radu & T. A. Shaposhnikova. (2011) Homogenization of the diffusion equation with nonlinear flux condition on the interior boundary of a perforated domain — the influence of the scaling on the nonlinearity in the effective sink-source term. Journal of Mathematical Sciences 179:3, pages 446-459.
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W. Jäger, M. Neuss-Radu & T. A. Shaposhnikova. (2011) Scale limit of a variational inequality modeling diffusive flux in a domain with small holes and strong adsorption in case of a critical scaling. Doklady Mathematics 83:2, pages 204-208.
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M. Lobo, M. E. Perez, V. V. Sukharev & T. A. Shaposhnikova. (2011) Averaging of boundary-value problem in domain perforated along (n − 1)-dimensional manifold with nonlinear third type boundary conditions on the boundary of cavities. Doklady Mathematics 83:1, pages 34-38.
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A. V. Podol’skii. (2010) Homogenization limit for the boundary value problem with the P-laplace operator and a nonlinear third boundary condition on the boundary of the holes in a perforated domain. Doklady Mathematics 82:3, pages 942-945.
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W. Jäger, M. Neuss-Radu & T. A. Shaposhnikova. (2010) Homogenization limit for the diffusion equation with nonlinear flux condition on the boundary of very thin holes periodically distributed in a domain, in case of a critical size. Doklady Mathematics 82:2, pages 736-740.
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MICOL AMAR, DANIELE ANDREUCCI, ROBERTO GIANNI & PAOLO BISEGNA. (2011) EVOLUTION AND MEMORY EFFECTS IN THE HOMOGENIZATION LIMIT FOR ELECTRICAL CONDUCTION IN BIOLOGICAL TISSUES. Mathematical Models and Methods in Applied Sciences 14:09, pages 1261-1295.
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Григорий Андроникович Иосифьян & Grigorii Andronikovich Iosif'yan. (2004) Об усреднении задач теории упругости с краевыми условиями СиньориниHomogenization of Elasticity Problems with Boundary Conditions of Signorini type. Математические заметки Matematicheskie Zametki 75:6, pages 818-833.
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D. Andreucci, P. Bisegna & E. DiBenedetto. (2003) Homogenization and concentrated capacity for the heat equation with non-linear variational data in reticular almost disconnected structures and applications to visual transduction. Annali di Matematica Pura ed Applicata 182:4, pages 375-407.
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