We study an electrical conduction problem in biological tissues in the radiofrequency range, which is governed by an elliptic equation with memory. We prove the time exponential asymptotic stability of the solution. We provide in this way both a theoretical justification to the complex elliptic problem currently used in electrical impedance tomography and additional information on the structure of the complex coefficients appearing in the elliptic equation. Our approach relies on the fact that the elliptic equation with memory is the homogenisation limit of a sequence of problems for which we prove suitable uniform estimates.

Amar, M., Andreucci, D., Bisegna, P., Gianni, R. (2009). Exponential asymptotic stability for an elliptic equation with memory arising in electrical conduction in biological tissues. EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 20, 431-459 [10.1017/S0956792509990052].

Exponential asymptotic stability for an elliptic equation with memory arising in electrical conduction in biological tissues

BISEGNA, PAOLO;
2009-01-01

Abstract

We study an electrical conduction problem in biological tissues in the radiofrequency range, which is governed by an elliptic equation with memory. We prove the time exponential asymptotic stability of the solution. We provide in this way both a theoretical justification to the complex elliptic problem currently used in electrical impedance tomography and additional information on the structure of the complex coefficients appearing in the elliptic equation. Our approach relies on the fact that the elliptic equation with memory is the homogenisation limit of a sequence of problems for which we prove suitable uniform estimates.
2009
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore ICAR/08 - SCIENZA DELLE COSTRUZIONI
Settore ING-IND/34 - BIOINGEGNERIA INDUSTRIALE
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
Exponential stability; equation with memory; impedance tomography;
Amar, M., Andreucci, D., Bisegna, P., Gianni, R. (2009). Exponential asymptotic stability for an elliptic equation with memory arising in electrical conduction in biological tissues. EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 20, 431-459 [10.1017/S0956792509990052].
Amar, M; Andreucci, D; Bisegna, P; Gianni, R
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/23546
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