Appearance of a Nonlocal Monotone Operator in Transmission Conditions when Homogenizing the Poisson Equation in a Domain Perforated Along an (n − 1)-Dimensional Manifold by Sets of Arbitrary Shape and Critical Size with Nonlinear Dynamic Boundary Conditions on the Boundary of Perforations

We construct and justify an efficient model arising when homogenizing the Poisson equation in an ε -periodically perforated domain along an ( n − 1)-dimensional manifold by sets of an arbitrary shape and critical size on the boundary of which we impose a nonlinear dynamic condition containing an abs...

Full description

Saved in:
Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 255; no. 4; pp. 423 - 443
Main Authors Zubova, M. N., Shaposhnikova, T. A.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.06.2021
Springer Nature B.V
Subjects
Absorptivity
Boundary conditions
Domains
Homogenization
Mathematics
Mathematics and Statistics
Nonlinear dynamics
Perforation
Poisson equation
Online AccessGet full text

Cover

More Information
Summary:We construct and justify an efficient model arising when homogenizing the Poisson equation in an ε -periodically perforated domain along an ( n − 1)-dimensional manifold by sets of an arbitrary shape and critical size on the boundary of which we impose a nonlinear dynamic condition containing an absorption coefficient of the form ε − k , where k takes the critical value ( n − 1)/( n − 2), n ≥ 3. We show that the transmission conditions on the manifold contain a nonlocal monotone operator.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-021-05382-7