2007.11785
OPTIMAL MANAGEMENT OF HARVESTED POPULATION AT THE EDGE OF EXTINCTION
Mickaël D. Chekroun, Honghu Liu
incompletemedium confidence
- Category
- math.DS
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:55 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s main estimate for the optimal-control error (Theorem 3.1) matches the claimed form with the [√(T−τ)+(T−τ)] factor and high-mode remainders, and is derived by invoking a general result (Theorem A.1) from CKL17; however, the local growth condition (A.14) required by that theorem is not verified for the KPPH problem and is not included among the hypotheses of Theorem 3.1, leaving a missing assumption in the stated result . The candidate model solution gives a plausible, adjoint/projection-based proof sketch that could circumvent (A.14), but it leaves crucial steps informal (definition of ε1N, ε2N and the adjoint Galerkin error bound that yields the [√(T−τ)+(T−τ)] factor). Thus, both are directionally correct but incomplete in rigor.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The manuscript cleanly specializes a general Galerkin optimal-control framework to an ecologically relevant semilinear PDE and provides both a uniform convergence result for trajectories and an explicit control-error estimate consistent with the literature. The verification of structural assumptions is careful. However, the main theorem as stated omits the local growth hypothesis required by the abstract result it invokes, and this key condition is not verified for the KPPH setting. Addressing this gap (or providing a direct adjoint/projection proof) would bring the paper to full rigor.