On Existence, Uniqueness and Two-Scale Convergence of a Model for Coupled Flows in Heterogeneous Media

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.

Automated summary

This paper investigates 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. Global weak solutions of the microscale problem are proven through semidiscretization in time, showing two-scale convergence as the scale parameter approaches zero. Emphasis is placed on the contribution of first order correctors in periodic homogenization and the uniqueness of solutions to the homogenized problem under additional assumptions.