Fast Reactions and Slow Manifolds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909130703241216 |
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| author | Kuehn, Christian Sulzbach, Jan-Eric |
| author_facet | Kuehn, Christian Sulzbach, Jan-Eric |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_09368 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fast Reactions and Slow Manifolds Kuehn, Christian Sulzbach, Jan-Eric Dynamical Systems Analysis of PDEs 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. |
| title | Fast Reactions and Slow Manifolds |
| topic | Dynamical Systems Analysis of PDEs |
| url | https://arxiv.org/abs/2301.09368 |