scholarly journals Asymptotic decay under nonlinear and noncoercive dissipative effects for electrical conduction in biological tissues

2016 ◽  
Vol 23 (4) ◽  
Author(s):  
Micol Amar ◽  
Daniele Andreucci ◽  
Roberto Gianni
Keyword(s):  
Electrical Conduction ◽  
Biological Tissues ◽  
Asymptotic Decay ◽  
Dissipative Effects

scholarly journals Homogenization limit and asymptotic decay for electrical conduction in biological tissues in the high radiofrequency range

2010 ◽  
Vol 9 (5) ◽  
pp. 1131-1160 ◽  
Author(s):  
Micol Amar ◽  
◽  
Daniele Andreucci ◽  
Paolo Bisegna ◽  
Roberto Gianni ◽  
...  
Keyword(s):  
Electrical Conduction ◽  
Biological Tissues ◽  
Asymptotic Decay

scholarly journals Exponential decay for a nonlinear model for electrical conduction in biological tissues

2016 ◽  
Vol 131 ◽  
pp. 206-228 ◽  
Author(s):  
M. Amar ◽  
D. Andreucci ◽  
R. Gianni
Keyword(s):  
Nonlinear Model ◽  
Exponential Decay ◽  
Electrical Conduction ◽  
Biological Tissues

scholarly journals Stability and memory effects in a homogenized model governing the electrical conduction in biological tissues

2009 ◽  
Vol 4 (2) ◽  
pp. 211-223 ◽  
Author(s):  
Micol Amar ◽  
Daniele Andreucci ◽  
Paolo Bisegna ◽  
Roberto Gianni
Keyword(s):  
Electrical Conduction ◽  
Biological Tissues ◽  
Memory Effects ◽  
Homogenized Model

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

2009 ◽  
Vol 20 (5) ◽  
pp. 431-459 ◽  
Author(s):  
M. AMAR ◽  
D. ANDREUCCI ◽  
P. BISEGNA ◽  
R. GIANNI
Keyword(s):  
Asymptotic Stability ◽  
Elliptic Equation ◽  
Electrical Conduction ◽  
Biological Tissues ◽  
Impedance Tomography ◽  
Uniform Estimates ◽  
Additional Information ◽  
Exponential Asymptotic Stability ◽  
Complex Coefficients ◽  
With Memory

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.

Homogenization limit for electrical conduction in biological tissues in the radio-frequency range

2003 ◽  
Vol 331 (7) ◽  
pp. 503-508 ◽  
Author(s):  
Micol Amar ◽  
Daniele Andreucci ◽  
Paolo Bisegna ◽  
Roberto Gianni
Keyword(s):  
Radio Frequency ◽  
Electrical Conduction ◽  
Biological Tissues ◽  
Frequency Range

Applications of homogenization techniques to the electrical conduction in biological tissues

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 2010013-2010014
Author(s):  
Micol Amar ◽  
Daniele Andreucci ◽  
Paolo Bisegna ◽  
Roberto Gianni
Keyword(s):  
Electrical Conduction ◽  
Biological Tissues

On The Construction of Models for Electrical Conduction in Biological Tissues

2010 ◽  
Author(s):  
F. Gómez-Aguilar ◽  
J. Bernal-Alvarado ◽  
T. Cordova-Fraga ◽  
J. Rosales-García ◽  
M. Guía-Calderón ◽  
...  
Keyword(s):  
Electrical Conduction ◽  
Biological Tissues

On a hierarchy of models for electrical conduction in biological tissues

2006 ◽  
Vol 29 (7) ◽  
pp. 767-787 ◽  
Author(s):  
M. Amar ◽  
D. Andreucci ◽  
P. Bisegna ◽  
R. Gianni
Keyword(s):  
Electrical Conduction ◽  
Biological Tissues ◽  
Hierarchy Of Models

EVOLUTION AND MEMORY EFFECTS IN THE HOMOGENIZATION LIMIT FOR ELECTRICAL CONDUCTION IN BIOLOGICAL TISSUES

2004 ◽  
Vol 14 (09) ◽  
pp. 1261-1295 ◽  
Author(s):  
MICOL AMAR ◽  
DANIELE ANDREUCCI ◽  
ROBERTO GIANNI ◽  
PAOLO BISEGNA
Keyword(s):  
Electrical Conduction ◽  
Electric Potential ◽  
Elliptic Equations ◽  
Potential Gradient ◽  
Biological Tissues ◽  
Dielectric Surface ◽  
Time Variable ◽  
Memory Effects ◽  
Spatial Period ◽  
History Of

We study a problem set in a finely mixed periodic medium, modelling electrical conduction in biological tissues. The unknown electric potential solves standard elliptic equations set in different conductive regions (the intracellular and extracellular spaces), separated by a dielectric surface (the cell membranes), which exhibits both a capacitive and a nonlinear conductive behaviour. Accordingly, dynamical conditions prevail on the membranes, so that the dependence of the solution on the time variable t is not only of parametric character. As the spatial period of the medium goes to zero, the electric potential approaches in a suitable sense a homogenization limit u0, which keeps the prescribed boundary data, and solves the equation [Formula: see text]. This is an elliptic equation containing a term depending on the history of the gradient of u0; the matrices B0, A1 in it depend on the microstructure of the medium. More exactly, we have that, in the limit, the current is still divergence-free, but it depends on the history of the potential gradient, so that memory effects explicitly appear. The limiting equation also contains a term ℱ keeping trace of the initial data.

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