Open AccessPARABOLIC PROBLEMS WITH DYNAMICAL BOUNDARY CONDITIONS IN PERFORATED MEDIA
Author(s) -
Claudia Timofte
Publication year - 2003
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2003.9637235
Subject(s) - mathematics , dirichlet boundary condition , mathematical analysis , boundary value problem , limit (mathematics) , robin boundary condition , domain (mathematical analysis) , homogeneous , boundary (topology) , heat equation , mixed boundary condition , parabolic partial differential equation , cauchy boundary condition , partial differential equation , combinatorics
The asymptotic behavior of the solution of a parabolic dynamical boundary‐value problem in a periodically perforated domain is analyzed. The perforations, which are identical and periodically distributed, are of size ϵ. In the perforated domain we consider a heat equation, with a Dirichlet condition on the exterior boundary and a dynamical boundary condition on the surface of the holes. The limit equation, as ϵ ? 0, is a heat equation with extra-terms coming from the influence of the non-homogeneous dynamical boundary condition.