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Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1

✍ Scribed by Durante, Tiziana; Mel’nyk, Taras A.


Book ID
118071019
Publisher
EDP Sciences
Year
2011
Tongue
English
Weight
435 KB
Volume
18
Category
Article
ISSN
1292-8119

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✍ Taras A. Mel'nyk 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 217 KB

## Abstract We consider a boundary‐value problem for the Poisson equation in a thick junction Ω~ε~, which is the union of a domain Ω~0~ and a large number of ε‐periodically situated thin curvilinear cylinders. The following nonlinear Robin boundary condition ∂~ν~__u__~ε~ + εκ(__u__~ε~)=0 is given o

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Convergence theorems and asymptotic estimates (as P0) are proved for eigenvalues and eigenfunctions of a mixed boundary value problem for the Laplace operator in a junction C of a domain and a large number N of -periodically situated thin cylinders with thickness of order "O(N\). We construct an ext