2020/10/10 by Brahim Amaziane, Amaziane, Brahim, Leonid Pankratov +3
Mathematics · #35B27 #35K65 #74Q15 #76M50 #76S05 #76T10 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #math.AP #math.PR #msc:35B27 #msc:35K65 #msc:74Q15 #msc:76M50 #msc:76S05 #msc:76T10
paper · pdf · doi:10.48550/arxiv.2010.05028
arxiv created 2020/10/10 · arxiv updated 2020/10/13
The paper deals with homogenization of a model problem describing an immiscible compressible two-phase flow in random statistically homogeneous porous media. We derive the effective (macroscopic) problem and prove the convergence of solutions. Our approach relies on stochastic two-scale convergence techniques, the realization-wise notion of stochastic two-scale convergence being used. Also, we exploit various a priori estimates as well as monotonicity and compactness arguments.