{"id":"W4409901602","doi":"10.3934/mcrf.2025026","title":"Carleman estimates for degenerate parabolic equations with single interior degeneracy point and applications","year":2025,"lang":"en","type":"article","venue":"Mathematical Control and Related Fields","topic":"Advanced Mathematical Modeling in Engineering","field":"Computer Science","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China; University of Alberta","keywords":"Degenerate energy levels; Degeneracy (biology); Mathematics; Single point; Point (geometry); Mathematical analysis; Parabolic partial differential equation; Mathematical physics; Physics; Geometry; Partial differential equation; Quantum mechanics; Limit (mathematics)","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001902851,0.001126103,0.0009923961,0.001966868,0.001044501,0.001169845,0.0009013523,0.001066648,0.002138315],"category_scores_gemma":[0.004647666,0.0004466503,0.001477203,0.0003816634,0.002583907,0.002314323,0.003477779,0.002147838,0.0001521425],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001086977,"about_ca_system_score_gemma":0.001031496,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003273703,"about_ca_topic_score_gemma":0.001704628,"domain_scores_codex":[0.9994953,0.0001621747,0.00002905769,0.00007222281,0.0001670863,0.00007423283],"domain_scores_gemma":[0.9982535,0.0007751192,0.000314027,0.0001013178,0.0003607562,0.0001952127],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00006877583,0.00006649194,0.001591269,0.0001603874,0.00005541111,0.0002895609,0.0005175472,0.07963473,0.01356127,0.8972901,0.00064725,0.006117142],"study_design_scores_gemma":[0.00001040144,0.00005015574,0.0004619755,0.0000294063,0.00001367256,0.00009617654,0.0001554803,0.7979326,0.00228273,0.1981375,0.0008007271,0.00002916894],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.1657185,0.0009233204,0.8078915,0.001148923,0.0001291462,0.00009022999,0.0001068669,0.0001331669,0.02385831],"genre_scores_gemma":[0.9552125,0.0006336792,0.03451334,0.0001703786,0.000104239,0.0001558817,0.00009664084,0.00005256602,0.00906091],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.003273703,"threshold_uncertainty_score":0.01006335,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.009460444139512386,"score_gpt":0.2425538995228691,"score_spread":0.2330934553833567,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}