Abstract
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.
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The first author is member of the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM), the second and the third author are members of the Gruppo Nazionale per la Fisica Matematica (GNFM) of the Istituto Nazionale di Alta Matematica (INdAM).
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Amar, M., Andreucci, D. & Gianni, R. Asymptotic decay under nonlinear and noncoercive dissipative effects for electrical conduction in biological tissues. Nonlinear Differ. Equ. Appl. 23, 48 (2016). https://doi.org/10.1007/s00030-016-0396-8
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DOI: https://doi.org/10.1007/s00030-016-0396-8