Effective transmission conditions for reaction-diffusion processes in domains separated by an interface
Neuss-Radu M, Jäger W (2007)
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2007
Journal
Book Volume: 39
Pages Range: 687-720
Journal Issue: 3
DOI: 10.1137/060665452
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 epsilon. By performing an asymptotic analysis with respect to the scale parameter epsilon we derive an effective model which consists of reaction-diffusion equations in two domains separated by an interface together with appropriate transmission conditions across the 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.
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
$\varepsilon.$ By performing an asymptotic analysis with respect to the
scale parameter $\varepsilon$ 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.
Read More: https://epubs.siam.org/doi/abs/10.1137/060665452?casa_token=8mgAtl16CJsAAAAA:AWP6wryXXeEfybHMoDiXWuWmHe7alFKC8xGQjLUJd95i5m5GH-gAlKRp0Saq2DLQBPwY30O71Is
Read More: https://epubs.siam.org/doi/abs/10.1137/060665452?casa_token=8mgAtl16CJsAAAAA:AWP6wryXXeEfybHMoDiXWuWmHe7alFKC8xGQjLUJd95i5m5GH-gAlKRp0Saq2DLQBPwY30O71Is
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
$\varepsilon.$ By performing an asymptotic analysis with respect to the
scale parameter $\varepsilon$ 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.
Read More: https://epubs.siam.org/doi/abs/10.1137/060665452?casa_token=8mgAtl16CJsAAAAA:AWP6wryXXeEfybHMoDiXWuWmHe7alFKC8xGQjLUJd95i5m5GH-gAlKRp0Saq2DLQBPwY30O71Is
Read More: https://epubs.siam.org/doi/abs/10.1137/060665452?casa_token=8mgAtl16CJsAAAAA:AWP6wryXXeEfybHMoDiXWuWmHe7alFKC8xGQjLUJd95i5m5GH-gAlKRp0Saq2DLQBPwY30O71Is
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
$\varepsilon.$ By performing an asymptotic analysis with respect to the
scale parameter $\varepsilon$ 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.
Read More: https://epubs.siam.org/doi/abs/10.1137/060665452?casa_token=8mgAtl16CJsAAAAA:AWP6wryXXeEfybHMoDiXWuWmHe7alFKC8xGQjLUJd95i5m5GH-gAlKRp0Saq2DLQBPwY30O71Is
Read More: https://epubs.siam.org/doi/abs/10.1137/060665452?casa_token=8mgAtl16CJsAAAAA:AWP6wryXXeEfybHMoDiXWuWmHe7alFKC8xGQjLUJd95i5m5GH-gAlKRp0Saq2DLQBPwY30O71Is
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Involved external institutions
Germany (DE)How to cite
APA:
Neuss-Radu, M., & Jäger, W. (2007). Effective transmission conditions for reaction-diffusion processes in domains separated by an interface. SIAM Journal on Mathematical Analysis, 39(3), 687-720. https://dx.doi.org/10.1137/060665452
MLA:
Neuss-Radu, Maria, and Willi Jäger. "Effective transmission conditions for reaction-diffusion processes in domains separated by an interface." SIAM Journal on Mathematical Analysis 39.3 (2007): 687-720.
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