  In the current paper the so-called REaction-DIffusion Manifold (REDIM) method
of model reduction is discussed within the framework of standard singular
perturbation theory. According to the REDIM a reduced model for the system
describing a reacting flow (accounting for chemical reaction, advection and
molecular diffusion) is represented by a low-dimensional manifold, which is
embedded in the system state space and approximates the evolution of the system
solution profiles in space and in time. This pure geometric construction is
reviewed by using Singular Perturbed System (SPS) theory as the only
possibility to formalize, to justify and to verify the suggested methodology.
The REDIM is studied as a correction by the diffusion of the slow invariant
manifold defined for a pure homogeneous system. A main result of the study is
an estimation of this correction to the slow invariant manifold. A benchmark
model of Mechaelis-Menten is extended to the system with the standard diffusion
described by the Laplacian and used as an illustration and for validation of
analytic results.
