Averaging of boundary-value problems for the Laplace operator in perforated domains with a nonlinear boundary condition of the third type on the boundary of cavities

DOI10.1007/s10958-013-1253-5zbMath1277.35145OpenAlexW2136886099MaRDI QIDQ384489

M. N. Zubova, Tatiana A. Shaposhnikova

Publication date: 27 November 2013

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-013-1253-5

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Theoretical approximation in context of PDEs (35A35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

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Cites Work

• On the homogenization of the Poisson equation in partially perforated domains with arbitrary density of cavities and mixed type conditions on their boundary
• Averaging the diffusion equation in a porous medium with weak absorption
• On homogenization problems for the Laplace operator in partially perforated domains with Neumann's condition on the boundary of cavities
• Asymptotic analysis of a parabolic semilinear problem with nonlinear boundary multiphase interactions in a perforated domain
• Averaging in a perforated domain with an oscillating third boundary condition
• Γ-convergence approach to variational problems in perforated domains with Fourier boundary conditions
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