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Stability and memory
effects in a homogenized model governing the electrical
conduction in biological tissues
Micol Amar, Daniele Andreucci, Paolo Bisegna and Roberto Gianni |
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Vol. 4 (2009), No. 2, 211–223
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Abstract |
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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
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Milestones
Received: 18 December 2007
Revised: 16 July 2008
Accepted: 3 November 2008
Published: 12 April 2009
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Authors |
| Micol Amar | |
| University of Rome La Sapienza Department of Mathematical Methods and Models Via Antonio Scarpa 16 00161 Rome Italy |
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| Daniele Andreucci | |
| University of Rome La Sapienza Department of Mathematical Methods and Models Via Antonio Scarpa 16 00161 Rome Italy |
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| Paolo Bisegna | |
| University of Rome Tor Vergata Department of Civil Engineering via del Politecnico 1 00133 Rome Italy |
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| Roberto Gianni | |
| University of Rome La Sapienza Department of Mathematical Methods and Models Via Antonio Scarpa 16 00161 Rome Italy |
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