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; Melnyk, T. A.. - 63:(2005), pp. 207-215. (Intervento presentato al convegno Fifth European Conference on Elliptic and Parabolic Problem: A Special Tribute to the Work of Haim Brezis tenutosi a Gaeta (IT) nel May 30- June 3, 2004).
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
