Calculus of Variations and Geometric Measure Theory
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M. Amar - D. Andreucci - P. Bisegna - R. Gianni

On a hierarchy of models for electrical conduction in biological tissues

created by amar on 12 Jul 2005
modified on 29 May 2006


Published Paper

Inserted: 12 jul 2005
Last Updated: 29 may 2006

Journal: Mathematical Methods in the Applied Sciences
Volume: 29
Pages: 767-787
Year: 2006


In this paper we derive a hierarchy of models for electrical conduction in a biological tissue, which is represented by a periodic array of period $\epsilon$ of conducting phases surrounded by dielectric shells of thickness $\epsilon\eta$ included in a conductive matrix. Such a hierarchy will be obtained from the Maxwell equations by means of a concentration process $\eta\to 0$, followed by a homogenization limit with respect to $\eps$. These models are then compared with regard to their physical meaning and mathematical issues.


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