Paper Info
Title
Effective Transmission Conditions for Reaction-Diffusion Processes in Domains Separated by an Interface
Abstract
In this paper, we develop multiscale methods appropriate for the homogenization of processes in domains containing thin heterogeneous layers. Our model problem consists of a nonlinear reaction-diffusion system defined in such a domain, and properly scaled in the layer region. Both the period of the heterogeneities and the thickness of the layer are of order e. By performing an asymptotic analysis with respect to the scale parameter e we derive an effective model which consists of the reaction-diffusion equations on two domains separated by an interface together with appropriate transmission conditions across this interface. These conditions are determined by solving local problems on the standard periodicity cell in the layer. Our asymptotic analysis is based on weak and strong two-scale convergence results for sequences of functions defined on thin heterogeneous layers. For the derivation of the transmission conditions, we develop a new method based on test functions of boundary layer type.
Year
DOI
Venue
2007
10.1137/060665452
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Keywords
Field
DocType
nonlinear reaction-diffusion systems,thin heterogeneous layer,homogenization,two-scale convergence,transmission conditions
Convergence (routing),Diffusion process,Weak convergence,Mathematical optimization,Nonlinear system,Mathematical analysis,Homogenization (chemistry),Boundary layer,Reaction–diffusion system,Asymptotic analysis,Mathematics
Journal
Volume
Issue
ISSN
39
3
0036-1410
Citations 
PageRank 
References 
10
1.26
0
Authors
2
Name
Order
Citations
PageRank
Maria Neuss-Radu1123.47
Willi Jäger2628.19