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In the context of periodic homogenization based on two-scale convergence, we homogenize a linear system of four coupled reaction-diffusion equations, two of which are defined on a manifold. The system describes the most important subprocesses modeling the carcinogenesis of a human cell caused by Benzo-[a]-pyrene molecules. These molecules are activated to carcinogens in a series of chemical reactions at the surface of the endoplasmic reticulum, which constitutes a fine structure inside the cell....
In this paper, a singular semi-linear parabolic PDE with locally periodic
coefficients is homogenized. We substantially weaken previous assumptions on
the coefficients. In particular, we prove new ergodic theorems. We show that
in such a weak setting on the coefficients, the proper statement of the
homogenization property concerns viscosity solutions, though we need a
bounded Lipschitz terminal condition.
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