Diminishing functionals for nonclassical entropy solutions selected by kinetic relations
Bibliographic record
Abstract
We consider nonclassical entropy solutions to hyperbolic conservation laws with concave-convex flux functions, whose undercompressive shocks are selected by a kinetic function φ^♭ . Extending earlier work of Baiti, LeFloch and Piccoli, we reinterpret their construction of the (generalized) strength of classical and nonclassical shocks, allowing us to simplify it, highlight its true nature and identify new degrees of freedom. Relying mainly upon the natural assumption that the composite function φ^♭ ◦ φ^♭ is uniformly contracting, we establish that the generalized total variation of front-tracking approximations is non-increasing in time, and we conclude with the existence of nonclassical solutions to the initial value problem. We also propose a definition of a generalized interaction potential, and investigate its monotonicity properties. In particular, we established that the interaction functional is globally non-increasing along a splitting-merging interaction pattern.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".