2209.01735
Maximal Domains of Solutions for Analytic Quasilinear Differential Equations of First Order
Chong-Kyu Han, Taejung Kim
correcthigh confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s Theorem 3.3 derives the maximal analytic extension and domain via invariant hypersurfaces built from first integrals and the analytic implicit function theorem; the candidate solution follows the same route and supplies an explicit transversality argument to ensure Fu ≠ 0 on the initial set, a detail that is only implicit in the paper. Apart from this added justification, the approaches and conclusions coincide.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The paper gives a concise and correct characterization of maximal analytic extensions for first-order quasilinear PDEs under a natural first-integral hypothesis, blending invariant-submanifold ideas with the analytic implicit function theorem. The results are correct and the exposition is clear, with instructive examples. One small but conceptually important detail—verifying Fu ≠ 0 on the initial set for the constructed invariant hypersurface—should be stated explicitly to render the proof of (i) entirely self-contained.