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Dr. Mariya Ptashnyk (Dept. of Mathematics I, RWTH Aachen)
| Speaker: |
Dr. Mariya Ptashnyk
(Department of Mathematics I, RWTH Aachen)
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| Date: |
Wednesday November 25, 2009
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| Title: |
Derivation of a
macroscopic receptor-based model using homogenization
techniques
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Abstract
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We study the problem of
diffusive transport of biomolecules in the intercellular space, modeled
as porous medium, and of their binding to the receptors located on the
surface membranes of the cells.
Cells are distributed periodically in a bounded domain. To describe
this microscopic process, defined on the scale of a cell, we introduce
a reaction-diffusion equation coupled with nonlinear ordinary
differential equations on the surface of the microstructure (on the
cells surface).
We consider the limit, when the number of cells tends to infinity and
at the same time their size tends to zero, while the volume fraction of
the cells remains fixed. Using the two-scale convergence, we prove the
convergence of the sequence of solutions of the microscopic problem to
the solution of the macroscopic equations. To show the convergence of
the nonlinear terms on the surfaces we use the unfolding method.
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