Global Dynamics of Reaction-Diffusion Systems with a Time-Varying Domain
Bibliographic record
Abstract
Abstract. This paper is devoted to the study of the global dynamics for a large class of reaction-diffusion systems with a time-varying domain. By appealing to the theories of asymptotically autonomous and periodic semiflows, we establish the threshold-type results on the long-time behavior of solutions for such a system in the cases of asymptotically bounded and periodic domains, respectively. To investigate the model system in the case of asymptotically unbounded domain, we first prove the global attractivity for nonautonomous reaction-diffusion systems with asymptotically vanishing diffusion coefficients via the method of sub- and supersolutions and then use the comparison arguments to obtain the threshold dynamics. We also apply these analytical results to a reaction-diffusion model of dengue fever transmission to investigate the effect of time-varying domain on the basic reproduction number. It turns out that the basic reproduction numbers with dengue fever transmission for the asymptotically bounded and unbounded domains are always less than that for the spatially homogeneous case, and under appropriate conditions, the basic reproduction numbers for asymptotically bounded and periodic domains are larger than or equal to that for the stationary bounded domain.
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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 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".