Inner‐Layer Asymptotics in Partially Perforated Domains: Coupling Across Flat and Oscillating Interfaces

The article examines a boundary‐value problem in a bounded 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 , we analyze the limit behavior of the problem as . 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 Sobolev space . Furthermore, for the ‐periodically oscillating interface of amplitude , we provide an approximation to the solution, detect the impact of the interface in the second term of the asymptotics, and establish the corresponding asymptotic estimates in ‐Sobolev spaces.