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arXiv · 2301.09368

Fast Reactions and Slow Manifolds

Christian Kuehn·Jan-Eric Sulzbach
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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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Christian Kuehn, Jan-Eric Sulzbach. 2023-01-23. Fast Reactions and Slow Manifolds. https://arxiv.org/abs/2301.09368

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