September/October 2013 A hierarchy of models for the electrical conduction in biological tissues via two-scale convergence: the nonlinear case
M. Amar, D. Andreucci, P. Bisegna, R. Gianni
Differential Integral Equations 26(9/10): 885-912 (September/October 2013). DOI: 10.57262/die/1372858555

Abstract

We study a hierarchy of electrical conduction problems in biological tissues. These problems are set in a finely mixed periodic medium, and the unknown electric potentials solve standard elliptic equations set in different conductive regions (the intracellular and extracellular spaces), separated by an interface (the cell membranes), which exhibits a capacitive and a nonlinear conductive behavior, due to its biochemical structure. Different scalings in the interface condition correspond to different problems in the hierarchy. As the spatial period of the medium goes to zero, the problems approach a homogenization limit depending on the initial scaling. The macroscopic models are obtained by using the technique of two-scale convergence.

Citation

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M. Amar. D. Andreucci. P. Bisegna. R. Gianni. "A hierarchy of models for the electrical conduction in biological tissues via two-scale convergence: the nonlinear case." Differential Integral Equations 26 (9/10) 885 - 912, September/October 2013. https://doi.org/10.57262/die/1372858555

Information

Published: September/October 2013
First available in Project Euclid: 3 July 2013

zbMATH: 1299.35041
MathSciNet: MR3100070
Digital Object Identifier: 10.57262/die/1372858555

Subjects:
Primary: 35B27 , 35B40 , 45K05 , 92C55

Rights: Copyright © 2013 Khayyam Publishing, Inc.

Vol.26 • No. 9/10 • September/October 2013
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