Asymptotic analysis of a boundary-value problem in a thin cascade domain with a local joint
| Autor: | Klevtsovskiy, A. V., Mel'nyk, T. A. |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Asymptotic Analysis, Vol. 97 (2016) 265-290 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.3233/ASY-151352 |
| Popis: | A nonuniform Neumann boundary-value problem is considered for the Poisson equation in a thin domain $\Omega_\varepsilon$ coinciding with two thin rectangles connected through a joint of diameter ${\cal O}(\varepsilon)$. A rigorous procedure is developed to construct the complete asymptotic expansion for the solution as the small parameter $\varepsilon \to 0.$ Energetic and uniform pointwise estimates for the difference between the solution of the starting problem $(\varepsilon >0)$ and the solution of the corresponding limit problem $(\varepsilon =0)$ are proved, from which the influence of the geometric irregularity of the joint is observed. Comment: 25 pages, 5 figures |
| Databáze: | arXiv |
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