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 homogenization limit of a sequence of problems for which we prove suitable uniform estimates.
Exponential asymptotic stability for an elliptic equation with memory arising in electrical conduction / Amar, Micol; Andreucci, Daniele; Bisegna, P.; Gianni, R.. - In: EUROPEAN JOURNAL OF APPLIED MATHEMATICS. - ISSN 0956-7925. - 20:(2009), pp. 431-459. [10.1017/S0956792509990052]
Exponential asymptotic stability for an elliptic equation with memory arising in electrical conduction
AMAR, Micol;ANDREUCCI, Daniele;R. GIANNI
2009
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 homogenization limit of a sequence of problems for which we prove suitable uniform estimates.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.