We construct and justify an efficient model arising when homogenizing the Poisson equation in an ε-periodically perforated domain along an (n − 1)-dimensional manifold by sets of an arbitrary shape and critical size on the boundary of which we impose a nonlinear dynamic condition containing an absorption coefficient of the form ε−k, where k takes the critical value (n − 1)/(n − 2), n ≥ 3. We show that the transmission conditions on the manifold contain a nonlocal monotone operator.
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Translated from Problemy Matematicheskogo Analiza 108, 2021, pp. 65-82.
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Zubova, M.N., Shaposhnikova, T.A. Appearance of a Nonlocal Monotone Operator in Transmission Conditions when Homogenizing the Poisson Equation in a Domain Perforated Along an (n − 1)-Dimensional Manifold by Sets of Arbitrary Shape and Critical Size with Nonlinear Dynamic Boundary Conditions on the Boundary of Perforations. J Math Sci 255, 423–443 (2021). https://doi.org/10.1007/s10958-021-05382-7
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DOI: https://doi.org/10.1007/s10958-021-05382-7