English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We concentrate on a model diffusion equation on a Lipschitz simply connected bounded domain with a small diffusion coefficient in a Lipschitz simply connected subdomain located strictly inside of the original domain. We study asymptotic properties of the solution with respect to the small diffusion coefficient vanishing. It is known that the solution asymptotically turns into a solution of a corresponding diffusion equation with Neumann boundary conditions on a part of the boundary. One typical proof technique of this fact utilizes a reduction of the problem to the interface of the subdomain, using a transmission condition. An analogous approach appears in studying domain decomposition methods without overlap, reducing the investigation to the surface that separates the subdomains and in theoretical foundation of a fictitious domain, also called embedding, method, e.g., to prove a classical estimate that guaranties convergence of the solution of the fictitious domain problem to the solution of the original Neumann boundary value problem.

Analysis of transmission problems on Lipschitz boundaries in stronger norms