Homogenization of the Neumann problem in thick multi‐structures of type 3 : 2 : 2

Abstract

SUMMARYUsing some special extension operator, a convergence theorem is proved for the solution to the Neumann boundary value problem for the Ukawa equation in a junction , which is the union of a domain 0 and a large number N of -periodically situated thin annular disks with variable thickness of order = O(N −1 ), as → 0.

Homogenization of a boundary‐value problem with a nonlinear boundary condition in a thick junction of type 3:2:1

“…Boundaryvalue problems in thick junctions are now very extensively investigated (see [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]). Sometimes G ε (i, j) = x ∈ R 3 : 0<x 3 <h,…”

Homogenization of the Robin problem in a thick multilevel junction

“…It follows from these assumptions that there exist positive constants m 0 and M 0 such that 0 < m 0 ≤ h 1 (x 2 ) < δ 0 and |h 1 ( (1) 1 Università degli Studi di Napoli Federico II, Napoli, Italia. 2 Let us divide the segment [0, a] into N equal segments [εj, ε(j + 1)], j = 0, .…”

“…Taking into account the properties of h 1 , its derivative [see (1)], and estimate (29) and using (26) and (27), we get…”

“…The asymptotic methods developed in [1][2][3] are used. A spectral problem in a plane thick multilevel junction with the flat boundaries of the thin rods was considered in [4].…”

Derivation of a macroscopic model for nutrient uptake by hairy-roots

“…The effective behavior of solutions of Laplace equation in a partially perforated domain and the contact problem between a porous medium and a non-perforated domain were studied in [14,15]. Derivation of macroscopic equations in a domain with a microstructure consisting of thick junctions is based on the construction of a proper extension operator, [16].…”