We propose two different approaches for asymptotic analysis of the Neumann boundary-value problem for the Ukawa equation in a thick multi-structure Omega(epsilon), which is the union of a domain Omega(0) and a large number N of epsilon-periodically situated thin annular disks with variable thickness of order epsilon = O(N-1), as epsilon -> 0. In the first approach, using some special extension operator, the convergence theorem is proved as epsilon -> 0. In the second one, the leading terms of the asymptotic expansion for the solution are constructed and the corresponding estimates in the Sobolev space H-1(Omega(epsilon)) are proved.

Asymptotic Analysis of the Neumann Problem for the Ukawa Equation in a Thick Multi-structure of Type 3:2:2

DE MAIO, UMBERTO;
2005

Abstract

We propose two different approaches for asymptotic analysis of the Neumann boundary-value problem for the Ukawa equation in a thick multi-structure Omega(epsilon), which is the union of a domain Omega(0) and a large number N of epsilon-periodically situated thin annular disks with variable thickness of order epsilon = O(N-1), as epsilon -> 0. In the first approach, using some special extension operator, the convergence theorem is proved as epsilon -> 0. In the second one, the leading terms of the asymptotic expansion for the solution are constructed and the corresponding estimates in the Sobolev space H-1(Omega(epsilon)) are proved.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/183900
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