Asymptotic expansion for the solution to a boundary-value problem in a thin cascade domain with a local joint

作者：Klevtsovskiy A V; Mel'nyk T A^*

来源：Asymptotic Analysis, 2016, 97(3-4): 265-290.

DOI：10.3233/ASY-151352

• asymptotic expansion
• asymptotic estimate
• thin domain with a local geometrical irregularity

A nonuniform Neumann boundary-value problem is considered for the Poisson equation in a thin domain Omega(epsilon) coinciding with two thin rectangles connected through a joint of diameter O(epsilon). A rigorous procedure is developed to construct the complete asymptotic expansion for the solution as the small parameter epsilon -> 0. Energetic and uniform pointwise estimates for the difference between the solution of the starting problem (epsilon > 0) and the solution of the corresponding limit problem (epsilon = 0) are proved, from which the influence of the geometric irregularity of the joint is observed.

• 出版日期2016