{"id":"W3029891775","doi":"10.1007/s00498-020-00258-8","title":"A weak maximum principle-based approach for input-to-state stability analysis of nonlinear parabolic PDEs with boundary disturbances","year":2020,"lang":"en","type":"article","venue":"Mathematics of Control Signals and Systems","topic":"Stability and Controllability of Differential Equations","field":"Engineering","cited_by":11,"is_retracted":false,"has_abstract":false,"ca_institutions":"Polytechnique Montréal","funders":"","keywords":"Nonlinear system; Partial differential equation; Mathematics; Maximum principle; Boundary (topology); Parabolic partial differential equation; Boundary value problem; Stability (learning theory); Mathematical analysis; Applied mathematics; Mathematical optimization; Computer science; Physics; Optimal control","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":[0.0005708052,0.0002148778,0.001231499,0.0001070136,0.00005870662,0.00006641343,0.0001685937,0.00005835281,0.00000882358],"category_scores_gemma":[0.0001915924,0.000166535,0.0002107431,0.0004184321,0.0001239103,0.00006330379,0.00001307658,0.00006706669,3.165325e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001841131,"about_ca_system_score_gemma":0.00005233681,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002670528,"about_ca_topic_score_gemma":0.0000400356,"domain_scores_codex":[0.9983203,0.00007129885,0.0008344931,0.0002509978,0.0003105867,0.0002122762],"domain_scores_gemma":[0.9984026,0.0006751276,0.0002132432,0.0003060293,0.0002558784,0.00014713],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0007359181,0.0006126194,0.007482943,0.01105428,0.003530729,2.617971e-7,0.004482496,0.9538693,0.01576234,0.001709868,0.000008280477,0.0007509555],"study_design_scores_gemma":[0.001493891,0.0002907769,0.001004804,0.00006088912,0.000833305,1.398272e-7,0.0005025966,0.9944286,0.0007336189,0.0003969667,0.00007580691,0.0001785489],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4026887,0.0004727201,0.5949944,0.00008270001,0.00001384027,0.001122623,0.0005225174,0.00003932097,0.00006322223],"genre_scores_gemma":[0.9939192,0.000003478971,0.005735967,0.00001957992,0.00002472958,0.0002481364,0.00002682381,0.00001963159,0.000002470023],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.5912305,"threshold_uncertainty_score":0.6791098,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02661652582446499,"score_gpt":0.2379842896881385,"score_spread":0.2113677638636735,"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."}}