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Approximation of Solutions of the Neumann Problem in Disintegrating Domains
Author(s) -
Maz'Ya V. G.,
Hänler M.
Publication year - 1993
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19931620120
Subject(s) - mathematics , limit (mathematics) , domain (mathematical analysis) , neumann boundary condition , boundary value problem , mathematical analysis , boundary (topology) , boundary layer , mechanics , physics
This article deals with approximation of solutions of the Neumann problem in domains, where small tubes are cut out. With an increasing number of tubes some kind of a porous layer inside the domain is approximated. Our aim is to find an asymptotic solution for the separated limit domains. We show that this asymptotics is described by a boundary value problem for the two limit domains, where the solutions for each domain are connected by the boundary conditions.