Fast Reactions and Slow Manifolds
arXiv (Cornell University)(2023)
Abstract
In this paper we generalize the Fenichel theory for attracting critical/slow
manifolds to fast-reaction systems in infinite dimensions. In particular, we
generalize the theory of invariant manifolds for fast-slow partial differential
equations in standard form to the case of fast reaction terms. We show that the
solution of the fast-reaction system can be approximated by the corresponding
slow flow of the limit system. Introducing an additional parameter that stems
from a splitting in the slow variable space, we construct a family of slow
manifolds and we prove that the slow manifolds are close to the critical
manifold. Moreover, the semi-flow on the slow manifold converges to the
semi-flow on the critical manifold. Finally, we apply these results to an
example and show that the underlying assumptions can be verified in a
straightforward way.
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Key words
slow manifolds,fast reactions
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