Discrete Study of the Blow-up Time of the Solution of Certain Non-Linear Parabolic Equations with Non-Linear Boundary Conditions
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Bibliographic record
Abstract
In this research work, we are interested in the discrete study of the blow-up time of the solution of certain nonlinear parabolic Partial Differential Equations (PDEs) subject to nonlinear boundary conditions. We have been able to establish the necessary and sufficient conditions under which the discrete solution of the problem blows up in a finite discrete time and, at the same time, we have given an estimate of this blow up time. Also, using a convergence study, we showed that the discrete time and solution converge respectively to the continuous time and solution when the discretization steps in space and time tend towards zero. Finally, we illustrated our analysis with graphical representations and some numerical results.
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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 | 0.007 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.002 |
| 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