2404.17220
Infinite dimensional Slow Manifolds for a Linear Fast-Reaction System
Christian Kuehn, Pascal Lehner, Jan-Eric Sulzbach
incompletemedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper correctly derives the slow manifold in Fourier space and proves existence, O(ε) Hausdorff convergence, and restricted flow convergence; however, it prints an explicit invariant-manifold formula in physical space missing the µ and ν terms and contains sign/label inconsistencies between w±, CF_ε, and C±_ε. The candidate fixes these (derives the necessary quadratic for L(ε) and shows invariance/exponential attraction directly), and the solution aligns with the correct (Fourier-consistent) formula. See the Fourier-space manifold CF_ε with µ, ν included, Lemma 3.1 and its eigenvectors and limits, contrasted with the misprinted C±_ε formula and subsequent uses in Theorem 3.3 (i)–(iii) .
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions \textbf{Journal Tier:} specialist/solid \textbf{Justification:} Strong expository contribution showing explicit slow manifolds for a linear fast-reaction PDE system, with clear links to Fourier-mode ODE analysis and semigroup estimates. The main mathematical ideas are correct, but the manuscript contains nontrivial typographical inaccuracies in the explicit formula for the invariant manifolds in physical variables (omitting µ and ν) and inconsistent ± labeling of eigenvectors/branches. These should be fixed to maintain clarity and correctness.