Input-to-state stability and integral input-to-state stability in various norms for 1-D nonlinear parabolic PDEs
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Bibliographic record
Abstract
For any p∈[1,+∞] and any r∈[p,+∞], by using the approximative Lyapunov method, the Lr-integral input-to-state stability (Lr-iISS) in the spatial Lp-norm for a class of 1-D nonlinear parabolic PDEs with distributed in-domain disturbances and under homogeneous Robin boundary conditions is assessed. Furthermore, when p∈[1,+∞), under additional assumptions on the relationship between the coefficients of the equation and the parameter p, the Lr-iISS in the spatial W1,p-norm for the consider system is proved. In addition, in the special case of p∈[2,+∞), a refined Lr-iISS estimate in the spatial W1,p-norm is established for the considered system.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it