{"id":"W4391546707","doi":"10.3934/cam.2024009","title":"Well-posedness and stability for a nonlinear Euler-Bernoulli beam equation","year":2024,"lang":"en","type":"article","venue":"Communications in Analysis and Mechanics","topic":"Stability and Controllability of Differential Equations","field":"Engineering","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"Polytechnique Montréal","funders":"Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China","keywords":"Bernoulli's principle; Nonlinear system; Stability (learning theory); Beam (structure); Euler's formula; Mathematics; Mathematical analysis; Applied mathematics; Physics; Computer science; Thermodynamics; Optics","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":[0.001446483,0.0008661507,0.0006045855,0.0006521365,0.0004402419,0.0009907485,0.0006301177,0.001003828,0.001580635],"category_scores_gemma":[0.002987944,0.0002376176,0.0007465795,0.0002767953,0.001535134,0.001317162,0.001280355,0.001134229,0.0001640369],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006635785,"about_ca_system_score_gemma":0.0007555104,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003526304,"about_ca_topic_score_gemma":0.001387248,"domain_scores_codex":[0.9996738,0.0001157031,0.00001755452,0.00007023381,0.00009342942,0.00002925458],"domain_scores_gemma":[0.9989437,0.0006368226,0.0001267331,0.00003225523,0.000207519,0.00005295235],"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":[0.0001169578,0.00008069252,0.002165445,0.0002598165,0.00008134959,0.0005624589,0.0007030785,0.4049547,0.04120278,0.5362589,0.001239458,0.01237438],"study_design_scores_gemma":[0.000006180836,0.00003366963,0.0003464805,0.00001324181,0.00000766549,0.00003867878,0.00004678539,0.9649324,0.001356406,0.03273862,0.0004664857,0.00001345979],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1563331,0.001126169,0.8245243,0.001789747,0.0001783226,0.00006159989,0.0001388299,0.0000652638,0.01578271],"genre_scores_gemma":[0.9482935,0.001170139,0.03603074,0.0002300777,0.0001389867,0.0001484314,0.0001108707,0.00003344172,0.01384382],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003526304,"threshold_uncertainty_score":0.007649839,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04233421645129582,"score_gpt":0.2845773061083605,"score_spread":0.2422430896570646,"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."}}