Differential and Integral Equations

A hierarchy of models for the electrical conduction in biological tissues via two-scale convergence: the nonlinear case

M. Amar, D. Andreucci, P. Bisegna, and R. Gianni

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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.

Article information

Source
Differential Integral Equations, Volume 26, Number 9/10 (2013), 885-912.

Dates
First available in Project Euclid: 3 July 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1372858555

Mathematical Reviews number (MathSciNet)
MR3100070

Zentralblatt MATH identifier
1299.35041

Subjects
Primary: 35B40: Asymptotic behavior of solutions 35B27: Homogenization; equations in media with periodic structure [See also 74Qxx, 76M50] 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20] 92C55: Biomedical imaging and signal processing [See also 44A12, 65R10, 94A08, 94A12]

Citation

Amar, M.; Andreucci, D.; Bisegna, P.; Gianni, R. A hierarchy of models for the electrical conduction in biological tissues via two-scale convergence: the nonlinear case. Differential Integral Equations 26 (2013), no. 9/10, 885--912. https://projecteuclid.org/euclid.die/1372858555


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