Diffusion in two thin layers separated by a semi-permeable membrane converges, as the layer thickness tends to zero, to 2D diffusion on the membrane with jumps between its two sides, with the membrane permeability coefficients becoming jump intensities.
Bobrowski, Degenerate convergence of semigroups, Semigroup Forum 49 (1994), no
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Semigroup-theoretic approach to diffusion in thin layers separated by semi-permeable membranes
Diffusion in two thin layers separated by a semi-permeable membrane converges, as the layer thickness tends to zero, to 2D diffusion on the membrane with jumps between its two sides, with the membrane permeability coefficients becoming jump intensities.