We consider a nonlinear model for electrical conduction in biological
tissues. The nonlinearity appears in the interface condition prescribed on the
cell membrane.
  The purpose of this paper is proving asymptotic convergence for large times
to a periodic solution when time-periodic boundary data are assigned. The
novelty here is that we allow the nonlinearity to be noncoercive. We consider
both the homogenized and the non-homogenized version of the problem

Amar, Micol

Andreucci, Daniele

Gianni, Roberto

English

arXiv

Micol Amar

Daniele Andreucci

Roberto Gianni

Crossref

Nonlinear Differential Equations and Applications NoDEA

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

We study here a problem arising in electrical conduction in biological tissues. From a physical point of view it consists in the study of the
electrical currents crossing a living tissue when an electrical potential is applied at the boundary.
Here the living tissue is regarded as a composite periodic domain made of extracellular and intracellular materials separated by a lipidic membrane which experiments prove to exhibit both conductive (due to ionic channels in the membrane) and capacitive behavior.
We study the asymptotic convergence to a periodic steady state of the microscopic and the macroscopic electric potential for large times.

We consider here the case where the conductive behavior of the cell membranes is nonlinear and monotone increasing but not coercive.
In order to achieve our goal, we proceed via a Liapunov-style technique so that the rate of convergence is not quantified

AMAR, Micol

ANDREUCCI, Daniele

R. Gianni

Archivio della ricerca- Università di Roma La Sapienza

Florence Research

https://flore.unifi.it/bitstream/2158/1111180/2/asymptotic%20decay%20under%20nonlinear%20and%20noncoercive.pdf

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

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

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Archivio della ricerca- Università di Roma La Sapienza

Florence Research