Well-posedness and stabilization of a model system for long waves posed\n on a quarter plane
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Bibliographic record
Abstract
In this paper we are concerned with a initial boundary-value problem for a\ncoupled system of two KdV equations, posed on the positive half line, under the\neffect of a localized damping term. The model arises when modeling the\npropagation of long waves generated by a wave maker in a channel. It is shown\nthat the solutions of the system are exponential stable and globally well-posed\nin the weighted space $L^2(e^{2bx}dx)$ for $b>0$. The stabilization problem is\nstudied using a Lyapunov approach while the well-posedness result is obtained\ncombining fixed point arguments and energy type estimates.\n
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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