Homogenization limit and asymptotic decay
for electrical conduction in biological tissues in the high radiofrequency range
Micol Amar - Università di Roma "La Sapienza", Via A. Scarpa 16, 00161 Roma, Italy (email)
Abstract: We derive a macroscopic model of electrical conduction in biological tissues in the high radio-frequency range, which is relevant in applications like electric impedance tomography. 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 solution for large times. Our results imply that periodic boundary data lead to an asymptotically periodic solution.
Keywords: Homogenization, electrical conduction in biological tissues, dynamical
boundary conditions, oscillating test-function method.
Received: September 2009; Revised: November 2009; Available Online: May 2010.
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