Abstract
When a diffusing substance interacts isothermally with an immobile solid phase, the resulting equations form a parabolic system of nonlinear partial differential equations for the nondimensional concentrations of the two phases. Introduction of the cumulative fluid concentration as a new dependent variable reduces the system to a scalar parabolic equation in which a small parameter multiplies the time derivative of the cumulative concentration. Omission of this term yields a pseudo-steady-state elliptic problem in which time appears only as a parameter in the boundary condition. The purpose of the paper is to rigorously justify this commonly used approximation. The major tools needed are suitable versions of the maximum principles for parabolic and elliptic equations.
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