What is it about?
A thin domain coinciding with two thin rectangles connected through a joint of small diameter is considered. A rigorous procedure is developed to construct the complete asymptotic expansion for the solution of a boundary-value problem in this thin domain as the thin domain is degenerated into an interval.
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Why is it important?
Energetic and uniform pointwise estimates for the difference between the solution of the starting problem and the solution of the corresponding limit problem, which we proved, show the influence of the geometric irregularity of the joint on the asymptotic behavior of the solution.
Perspectives
Such constructions of thin domains are successfully used in nanotechnologies, micro-technique, modern engineering constructions, as well as many physical and biological systems. Special interest of researchers is focused on various effects observed in vicinities of local irregularities of the geometry (widening or narrowing) of channels (e.g., adhesion to the walls, welds, and stenosis). Also the study of influence of local geometrical irregularities is very important in engineering, since such irregularities often directly affect the strength (stability, resistance, power, etc.) of constructions and devices.
Taras Mel'nyk
Kyyivs'kij nacional'nij universytet imeni Tarasa Shevchenka
Read the Original
This page is a summary of: Asymptotic expansion for the solution to a boundary-value problem in a thin cascade domain with a local joint, Asymptotic Analysis, April 2016, IOS Press,
DOI: 10.3233/asy-151352.
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