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

Article type: Research Article

Authors: Klevtsovskiy, A.V. | Mel’nyk, T.A.^{; *}

Affiliations: Department of Mathematical Physics, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska st., 64/13, Kyiv 01601, Ukraine. E-mails: avklevtsovskiy@gmail.com, melnyk@imath.kiev.ua

Correspondence: [*] Corresponding author. Tel.: +380-44-259 0540; Fax: +380-44-259 0785; E-mail: melnyk@imath.kiev.ua.

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

Keywords: asymptotic expansion, asymptotic estimate, thin domain with a local geometrical irregularity

DOI: 10.3233/ASY-151352

Journal: Asymptotic Analysis, vol. 97, no. 3-4, pp. 265-290, 2016