{"id":"W1997451771","doi":"10.1016/j.jmaa.2011.04.083","title":"Existence of weak positive solutions to a nonlinear PDE system around a triple phase boundary, coupling domain and boundary variables","year":2011,"lang":"en","type":"article","venue":"Journal of Mathematical Analysis and Applications","topic":"Advanced Mathematical Modeling in Engineering","field":"Computer Science","cited_by":7,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Ottawa","funders":"","keywords":"Mathematics; Mathematical analysis; Nonlinear system; Bounded function; Boundary (topology); Domain (mathematical analysis); Partial differential equation; Boundary value problem; Triple phase boundary; Fixed-point theorem; Coupling (piping); Physics; Electrolyte","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00074509,0.0001404757,0.0005527593,0.0002885172,0.0002046554,0.00009706701,0.000345592,0.00004722879,0.000004866056],"category_scores_gemma":[0.00009107598,0.00011224,0.0001452608,0.000821799,0.0001220613,0.0002539869,0.0001548501,0.0001412987,0.000002496868],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004482762,"about_ca_system_score_gemma":0.00005368083,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003454498,"about_ca_topic_score_gemma":0.000001417654,"domain_scores_codex":[0.9984823,0.00002050693,0.0008098588,0.0002140843,0.0002766524,0.0001966141],"domain_scores_gemma":[0.9985223,0.0003013378,0.0003518791,0.0003278105,0.0002640894,0.0002325229],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00002046323,0.0007203755,0.00002230369,0.0003387113,0.0005797275,0.000006101744,0.001583032,0.002531429,0.00264484,0.9899645,0.00000638613,0.001582118],"study_design_scores_gemma":[0.0004009214,0.0001574947,0.00005497995,0.0002930551,0.0005813778,0.0001390057,0.0007642327,0.8034001,0.0004555213,0.193474,0.0001088009,0.0001705382],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.02802312,0.0002538255,0.9709667,0.0001237406,0.00001298699,0.0002035802,0.00001376027,0.00002421942,0.0003780523],"genre_scores_gemma":[0.3038745,0.00001872792,0.6960166,0.00001248643,0.00003202183,0.00002663903,7.120219e-7,0.000006898073,0.00001142397],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.8008687,"threshold_uncertainty_score":0.4577012,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02442321227606486,"score_gpt":0.2733729554632945,"score_spread":0.2489497431872296,"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."}}