Variational approach of critical sharp front speeds in degenerate diffusion model with time delay
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Bibliographic record
Abstract
Abstract For the classical reaction diffusion equation, the a priori speed of fronts is determined exactly in the pioneering paper (Benguria and Depassier 1996 Commun. Math. Phys. 175 221–227) by variational characterization method. In this paper, we study the age-structured population dynamics using a degenerate diffusion equation with time delay. We show the existence and uniqueness of sharp critical fronts, where the sharp critical front is C 1 -smooth when the diffusion degeneracy is weaker with 1 < m < 2, and the sharp critical front is non- C 1 -smooth (piecewise smooth) when the diffusion degeneracy is stronger with m ⩾ 2, and the non-critical waves are C 2 -smooth. We give a new variational approach for the critical wave speed and investigate how the time delay affects the propagation mechanism of fronts. It is shown that the time delay slows down the critical wave speed.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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) | 0.001 | 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