Homogenization of the boundary value problem for the Laplace operator in a perforated domain with a rapidly oscillating nonhomogeneous Robin-type condition on the boundary of holes in the critical case

DOI10.1134/S1064562417040159zbMath1375.35030OpenAlexW2746742617MaRDI QIDQ2411794

M. N. Zubova, Tatiana A. Shaposhnikova

Publication date: 25 October 2017

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562417040159

zbMATH Keywords

rapidly oscillating nonhomogeneous Robin-type condition

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (3)

Optimal control and ``strange term arising from homogenization of the Poisson equation in the perforated domain with the Robin-type boundary condition in the critical case ⋮ Model of stationary diffusion with absorption in domains with fine-grained random boundaries ⋮ Homogenization of a boundary-value problem in a domain perforated by cavities of arbitrary shape with a general nonlinear boundary condition on their boundaries: the case of critical values of the parameters

Cites Work

• Unnamed Item
• Unnamed Item
• Homogenization of the \(p\)-Laplacian with nonlinear boundary condition on critical size particles: identifying the strange term for the some non smooth and multivalued operators
• Homogenization for the \(p\)-Laplace operator and nonlinear Robin boundary conditions in perforated media along \((n - 1)\)-dimensional manifolds
• Homogenization problem in a domain perforated by tiny isoperimetric holes with nonlinear Robin type boundary conditions
• 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
• Homogenization for the \(p\)-Laplacian in an \(n\)-dimensional domain perforated by very thin cavities with a nonlinear boundary condition on their boundary in the case \(p\) = \(n\)
• Homogenization of a variational inequality for the Laplace operator with nonlinear restriction for the flux on the interior boundary of a perforated domain
• Homogenization of variational inequalities of Signorini type for the \(p\)-Laplacian in perforated domains when \(p\in(1, 2)\)
• On critical parameters in homogenization of perforated domains by thin tubes with nonlinear flux and related spectral problems
• The Poisson Equation with Nonautonomous Semilinear Boundary Conditions in Domains with Many Time Holes
• On homogenization of nonlinear Robin type boundary conditions for cavities along manifolds and associated spectral problems

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