Differential and Integral Equations
- Differential Integral Equations
- Volume 26, Number 9/10 (2013), 885-912.
A hierarchy of models for the electrical conduction in biological tissues via two-scale convergence: the nonlinear case
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.
Differential Integral Equations, Volume 26, Number 9/10 (2013), 885-912.
First available in Project Euclid: 3 July 2013
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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