For systems of reacting and diffusing chemical species, we present a method based on geometric singular perturbation theory for finding invariant manifolds whose dimension is lower than that of the full phase space. We reduce large systems of reaction-diffusion PDE's to smaller systems of PDEs by keeping only a subset of the reacting species. Critical information about the removed species is naturally retained via nonlinear diffusion coefficients. We also present a PDE analog of Fraser's iterative method for ODEs arising in reaction kinetic theory.

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1999-2000 Reactive Flow and Transport Phenomena