期刊
COMPTES RENDUS MECANIQUE
卷 331, 期 7, 页码 503-508出版社
EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER
DOI: 10.1016/S1631-0721(03)00107-4
关键词
continuum mechanics; electrical conduction; homogenization; biomathematics
类别
We study an evolutive model for electrical conduction in biological tissues, where the conductive intra-cellular and extracellular spaces are separated by insulating cell membranes. The mathematical scheme is an elliptic problem, with dynamical boundary conditions on the cell membranes. The problem is set in a finely mixed periodic medium. We show that the homogenization limit u(0) of the electric potential, obtained as the period of the microscopic structure approaches zero, solves the equation -div(sigma(0)del(x)u(0) + A(0)del(x)u(0) + integral(0)(t) A(1)(t - tau)del(x)u(0)(x, tau)dtau - F(x, t)) = 0 where sigma(0) > 0 and the matrices A(0), A(1) depend on geometric and material properties, while the vector function F keeps trace of the initial data of the original problem. Memory effects explicitly appear here, making this elliptic equation of non standard type.
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