ISS methods for fully nonlinear PDEs
A question from SIAM Review (2020). Section 10.3; inspected PDF p. 70.
Editorial MSC2020 classification. Original article codes and source evidence are recorded in the literature directory.
Problem statement
Develop general input-to-state stability criteria for PDE evolution equations whose unbounded part is nonlinear. The survey proposes extending nonlinear-semigroup methods to robustness under inputs, beyond the semilinear framework with a Lipschitz perturbation of a linear generator.
Lean 4
No Lean statement or proof is attached yet. Have a formalization? Share its source to add it to this problem.
Background
Editorial summary of Section 10.3; inspected PDF p. 70 in Input-to-state stability of infinite-dimensional systems: recent results and open questions. Read the original for the full definitions and context.
SIAM Review 62 (2020), 529–614. These are research programmes from §10, not single yes/no conjectures. The older Dirichlet heat Lyapunov question is not extracted because later work addresses it.
Progress & source assessment
The source presents this question or research direction as unresolved at the time of writing. Current status has not been independently established. Source inspected on 2026-09-10; this date is a provenance check, not certification that the question remains open.
- [1]Andrii Mironchenko, Christophe Prieur. Input-to-state stability of infinite-dimensional systems: recent results and open questions. SIAM Review (2020). linkSection 10.3; inspected PDF p. 70
Recorded progress
Add yours →Nothing recorded yet. A pointer to a paper the entry is missing counts.
Machine attempts
0 recordedAttempts run against the statement below and are recorded in full, including the failures. The point is to stop the next model — and the next person — from re-walking a road that is already known to end. Each attempt costs 25 credits.
No machine attempts recorded.
Sign in to run an attempt. New accounts start with enough credits for ten.
Discussion
0 notesNotes are for clarifying the statement, flagging a missing reference, or recording why an approach fails. Claimed solutions belong in a submission, where they can be reviewed.
No notes yet.
Sign in to add a note.