Calculus of Variations and Geometric Measure Theory
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M. Amar - D. Andreucci - P. Bisegna - R. Gianni

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

created by amar on 05 Feb 2007
modified on 17 Mar 2010

[BibTeX]

Published Paper

Inserted: 5 feb 2007
Last Updated: 17 mar 2010

Journal: Euro. Jnl. of Applied Mathematics
Volume: 20
Pages: 431-459
Year: 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, providing in this way a theoretical justification to the complex elliptic problem currently used in electrical impedance tomography.

Our approach relies on the fact that the elliptic equation is the homogenization limit of a sequence of problems for which we are able to prove suitable uniform estimates.


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