New SFB 1313 publication, published in the scientific journal "Mathematical Methods of the Applied Sciences". The work has been developed in the context of the research project C02. The publiction gives an answer to the problem of detecting the impact of an oscillating interface in coupled systems.
Author
- Taras Mel'nyk (University of Stuttgart, SFB 1313 research project C02)
Abstract
The article examines a boundary-value problem in a bounded domain Ωε 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 ε → 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 Sobolev space H1 (Ωε). Furthermore, for the ε-periodically oscillating interface of amplitude O(ε), 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 H1-Sobolev spaces.