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Model of diffusion in partially fissured media. (English) Zbl 1017.35016
Summary: We consider an $$\varepsilon$$-periodic structure formed by two interwoven and connected components which stand for the fissure system and the porous matrix. We assume that on the matrix-fissure interface the pressure has a jump of order $$\varepsilon^{-1}$$ with respect to the fluid flux which is continuous. We prove that the corresponding homogenized system is exactly that proposed by G. I. Barenblatt, Yu. P. Zheltov and I. N. Kochina [PMM, J. Appl. Math. Mech. 24, 1286-1303 (1961; Zbl 0104.21702)].

##### MSC:
 35B27 Homogenization in context of PDEs; PDEs in media with periodic structure 76S05 Flows in porous media; filtration; seepage 76R50 Diffusion
##### Keywords:
diffusion problem; two-scale convergence
Zbl 0104.21702
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