Vol. 4, No. 2, 2009

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ISSN: 1559-3959
Stability and memory effects in a homogenized model governing the electrical conduction in biological tissues

Micol Amar, Daniele Andreucci, Paolo Bisegna and Roberto Gianni

Vol. 4 (2009), No. 2, 211–223
Abstract

We present a macroscopic model of electrical conduction in biological tissues. This model is derived via a homogenization limit by a microscopic formulation based on Maxwell’s equations, taking into account the periodic geometry of the microstructure. We also study the asymptotic behavior of the model for large times. Our results imply that periodic boundary data lead to an asymptotically periodic solution. The model is relevant to applications like electric impedance tomography.

Keywords
asymptotic decay, stability, homogenization, memory effects, electrical conduction, biological tissues
Milestones
Received: 18 December 2007
Revised: 16 July 2008
Accepted: 3 November 2008
Published: 12 April 2009
Authors
Micol Amar
University of Rome La Sapienza
Department of Mathematical Methods and Models
Via Antonio Scarpa 16
00161 Rome
Italy
Daniele Andreucci
University of Rome La Sapienza
Department of Mathematical Methods and Models
Via Antonio Scarpa 16
00161 Rome
Italy
Paolo Bisegna
University of Rome Tor Vergata
Department of Civil Engineering
via del Politecnico 1
00133 Rome
Italy
Roberto Gianni
University of Rome La Sapienza
Department of Mathematical Methods and Models
Via Antonio Scarpa 16
00161 Rome
Italy