GLOBAL ATTRACTORS FOR A FULL VON KARMAN BEAM TRANSMISSION PROBLEM

Tamara Fastovska

correctmedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper establishes well-posedness, asymptotic smoothness (under explicit parameter relations), and—crucially—the strictness of a Lyapunov functional via a nontrivial unique continuation argument based on Carleman estimates, then derives a compact global attractor for autonomous loads with g2 = g4 = 0. The candidate solution reproduces the energy identity and outlines quasi-stability and stationary estimates, but incorrectly treats the Lyapunov functional as strict without proving the required unique continuation from the damped to undamped subdomain; this step is essential and is precisely what the paper proves with Carleman estimates. The candidate’s stationary reduction also misstates the order of the reduced ODE. Hence the model’s proof is incomplete/incorrect on key points, while the paper’s argument is complete and correct.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The manuscript proves a nontrivial attractor result for a full von Kármán transmission beam with damping only on a subinterval. The methods combine quasi-stability type arguments with a carefully crafted Carleman estimate to establish a strict Lyapunov functional despite partial damping. The work is technically sound and contributes meaningfully to the literature on transmission problems. Minor editorial clarifications would improve readability (e.g., elaborating the stationary set bounds and streamlining some technical steps), but the core results are correct and of interest to specialists.