Monotone Multivalued Nonautonomous Dynamical Systems

José A. Langa, Jacson Simsen, Mariza Stefanello Simsen, José Valero

correcthigh confidence

Category: Not specified
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The candidate reproduces Theorem 5 of the uploaded paper almost step-for-step: it constructs extremal forward representatives from SOP with identical initial data, extracts pullback limits via K2+K4 and a diagonal argument to obtain complete orbits γ_* and γ^*, proves A(t) is squeezed between them, establishes u_- ≤ γ_* ≤ γ^* ≤ u_+, shows extremality among complete orbits, and derives asymptotic stability under forward uniqueness using the order–metric compatibility. These steps track the paper’s proof and hypotheses precisely.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

The main theorem rigorously generalizes the interval-structure characterization of attractors to nonautonomous multivalued SOP processes, including precise extremal complete orbits and their (conditional) asymptotic stability. The assumptions (K1),(K2),(K4) and the order–topology compatibility are natural and used optimally. The proof is clear and robust, though a short lemma formalizing the existence/uniqueness of SOP extremal representatives for identical initial data could improve readability. The applications to a PDE inclusion and the asymptotically autonomous limit further demonstrate significance.