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arXiv · 2504.02716

Inner-layer asymptotics in partially perforated domains: coupling across flat and oscillating interfaces

Taras Mel'nyk
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Abstract

The article examines a boundary-value problem in a domain consisting of perforated and imperforate regions, with Neumann conditions prescribed at the boundaries of the perforations. Assuming the porous medium has symmetric, periodic structure with a small period $\varepsilon,$ we analyse the limit behavior of the problem as $\varepsilon \to 0.$ A crucial aspect of this study is deriving correct coupling conditions at the common interface, which is achieved using inner-layer asymptotics. For the flat interface, we construct and justify a complete asymptotic expansion of the solution in the $H^1$-Sobolev space. Furthermore, for the $\varepsilon$-periodically oscillating interface of amplitude $\mathcal{O}(\varepsilon),$ we provide an approximation to the solution and establish the corresponding asymptotic estimates in $H^1$-Sobolev spaces.

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Taras Mel'nyk. 2025-04-03. Inner-layer asymptotics in partially perforated domains: coupling across flat and oscillating interfaces. https://doi.org/10.1002/mma.70310

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