In this work, a system of nonlinear (parabolic) partial differential equations (PDEs) incorporated with mixed Neumann-Robin boundary conditions (see (1.2)-(1.3)) are considered arising in case of transport processes, namely diffusion and reaction of chemical species, inside a porous medium. For this system, we establish the existence and uniqueness of the positive global weak solution and afterwards upscale this system from the micro to the macro scale to remove the heterogeneities of the medium by using two-scale convergence.

weak solution, semilinear parabolic equation, reversible reactions, Neumann-Robin boundary conditions, homogenization, two-scale convergence.