{"id":"W2328648075","doi":"10.3934/cpaa.2012.11.365","title":"On the solvability conditions for the diffusion equation with convection terms","year":2011,"lang":"en","type":"article","venue":"Communications on Pure &amp Applied Analysis","topic":"Spectral Theory in Mathematical Physics","field":"Mathematics","cited_by":51,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Work (physics); Operator (biology); Convection–diffusion equation; Convection; Heat equation; Mathematical analysis; Elliptic curve; Fredholm theory; Elliptic operator; Fredholm integral equation; Diffusion equation; Diffusion; Order (exchange); Physics; Integral equation; Thermodynamics","routes":{"ca_aff":true,"ca_fund":false,"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":[0.001217094,0.0009397213,0.0006577809,0.001248895,0.0008451488,0.001401385,0.0006180121,0.001474736,0.003069393],"category_scores_gemma":[0.00482773,0.000279063,0.0009486389,0.0002821435,0.001703794,0.002503676,0.002079361,0.001447192,0.0003758359],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005956818,"about_ca_system_score_gemma":0.0008206071,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001350658,"about_ca_topic_score_gemma":0.000721776,"domain_scores_codex":[0.9997112,0.00009573202,0.00002110463,0.00005670296,0.0000710872,0.00004422429],"domain_scores_gemma":[0.9980621,0.0011853,0.0002220163,0.00006386,0.0002823569,0.0001844236],"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":[0.000192115,0.0001271412,0.001653185,0.0002563228,0.00005008223,0.001251295,0.001022669,0.0479345,0.04225574,0.8911206,0.002480738,0.01165571],"study_design_scores_gemma":[0.00008529852,0.0001260964,0.0009608447,0.00006269972,0.00002027193,0.0003692014,0.0002697215,0.5082297,0.008751875,0.4785668,0.002499412,0.00005804812],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4570193,0.001530726,0.4925483,0.004133799,0.0002503005,0.0001934126,0.0005046878,0.0001956071,0.04362395],"genre_scores_gemma":[0.9485552,0.0007317823,0.03964754,0.0002888525,0.0003898924,0.0002201407,0.0004346437,0.0001294728,0.009602426],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003069393,"threshold_uncertainty_score":0.01026815,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1766759869569123,"score_gpt":0.3455824688650476,"score_spread":0.1689064819081353,"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."}}