Exponential decay for a nonlinear model for electrical conduction in biological tissues. (January 2016)

• Record Type: Journal Article
• Authors: Amar, M.; Andreucci, D.; Gianni, R.
• Is Part Of: Nonlinear analysis. Volume 131(2016)
• Page Start: 206
• Page End: 228
• Publication Date: 2016-01
• Subjects: 35B40 -- 35B27 -- 45K05 -- 92C55; Asymptotic decay -- Nonlinear homogenization -- Two-scale techniques; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.07.002
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the asymptotic convergence to a periodic steady state of the solution of a nonlinear system of equations with periodic boundary data modeling electrical conduction in biological tissues, both in the microscopic and in the homogenized version. Such model keeps into account the resistive behavior of the intracellular and extracellular domains and also the capacitive/resistive behavior of the lipidic cellular membrane. The rate of convergence is analyzed and the systems of equations satisfied by the asymptotic limits are exhibited, when the resistive behavior of the membrane is described by a strictly monotone and coercive nonlinear function. The special case of homogeneous boundary conditions is also investigated, where the coercivity assumption can be relaxed.