This paper is concerned with the global existence, uniqueness and homogenization of degenerate partial differential equations with integral conditions arising from coupled transport processes and chemical reactions in three-dimensional highly heterogeneous porous media. Existence of global weak solutions of the microscale problem is proved by means of semidiscretization in time deriving a priori estimates for discrete approximations needed for proofs of existence and convergence theorems. It is further shown that the solution of the microscale problem is two-scale convergent to that of the upscaled problem as the scale parameter goes to zero. In particular, we focus our efforts on the contribution of the so-called first order correctors in periodic homogenization. Finally, under additional assumptions, we consider the problem of the uniqueness of the solution to the homogenized problem.

本文关注的是退化的偏微分方程的整体存在性，唯一性和均质性，这些条件由三维高度非均质多孔介质中的耦合输运过程和化学反应引起，具有积分条件。微观问题的整体弱解的存在是通过时间上的半离散化来证明的，它为存在性和收敛定理的证明需要离散近似的先验估计。进一步表明，随着尺度参数变为零，微观尺度问题的解与尺度问题的解是两尺度收敛的。特别是，我们将精力集中在所谓的一阶校正器在周期性均质化方面的贡献上。最后，在其他假设下，