{"id":"https://openalex.org/W1999667664","doi":"https://doi.org/10.1109/acc.2014.6859467","title":"Discrepancy-based control of a heat equation with quadratic nonlinearity","display_name":"Discrepancy-based control of a heat equation with quadratic nonlinearity","publication_year":2014,"publication_date":"2014-06-01","ids":{"openalex":"https://openalex.org/W1999667664","doi":"https://doi.org/10.1109/acc.2014.6859467","mag":"1999667664"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2014.6859467","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2014.6859467","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2014 American Control Conference","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035541519","display_name":"Stefan Palis","orcid":"https://orcid.org/0000-0002-1941-2289"},"institutions":[{"id":"https://openalex.org/I95793202","display_name":"Otto-von-Guericke-Universit\u00e4t Magdeburg","ror":"https://ror.org/00ggpsq73","country_code":"DE","type":"education","lineage":["https://openalex.org/I95793202"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Stefan Palis","raw_affiliation_strings":["Otto von Guericke Universitat Magdeburg, Magdeburg, Sachsen-Anhalt, DE","Otto-von-Guericke-Universit\u00e4t Magdeburg, External Organizations"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Otto von Guericke Universitat Magdeburg, Magdeburg, Sachsen-Anhalt, DE","institution_ids":[]},{"raw_affiliation_string":"Otto-von-Guericke-Universit\u00e4t Magdeburg, External Organizations","institution_ids":["https://openalex.org/I95793202"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047484433","display_name":"Achim Kienle","orcid":"https://orcid.org/0000-0002-9011-0451"},"institutions":[{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"nonprofit","lineage":["https://openalex.org/I149899117"]},{"id":"https://openalex.org/I4210127568","display_name":"Max Planck Institute for Dynamics of Complex Technical Systems","ror":"https://ror.org/030h7k016","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210127568"]},{"id":"https://openalex.org/I95793202","display_name":"Otto-von-Guericke-Universit\u00e4t Magdeburg","ror":"https://ror.org/00ggpsq73","country_code":"DE","type":"education","lineage":["https://openalex.org/I95793202"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Achim Kienle","raw_affiliation_strings":["Otto von Guericke Universitat Magdeburg, Magdeburg, Sachsen-Anhalt, DE","Otto-von-Guericke-Universit\u00e4t Magdeburg, External Organizations","Process Synthesis and Process Dynamics, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Otto von Guericke Universitat Magdeburg, Magdeburg, Sachsen-Anhalt, DE","institution_ids":[]},{"raw_affiliation_string":"Otto-von-Guericke-Universit\u00e4t Magdeburg, External Organizations","institution_ids":["https://openalex.org/I95793202"]},{"raw_affiliation_string":"Process Synthesis and Process Dynamics, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society","institution_ids":["https://openalex.org/I4210127568","https://openalex.org/I149899117"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0899761,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":null,"first_page":"3359","last_page":"3362"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9772999882698059,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/heat-equation","display_name":"Heat equation","score":0.6696395874023438},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6578160524368286},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6483652591705322},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6363868713378906},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5652799606323242},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5640386939048767},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.533950686454773},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.49131909012794495},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.4194602966308594},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3943943381309509},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3019072711467743},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2701355814933777},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14969772100448608},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05258595943450928}],"concepts":[{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.6696395874023438},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6578160524368286},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6483652591705322},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6363868713378906},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5652799606323242},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5640386939048767},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.533950686454773},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.49131909012794495},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.4194602966308594},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3943943381309509},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3019072711467743},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2701355814933777},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14969772100448608},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05258595943450928},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/acc.2014.6859467","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2014.6859467","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2014 American Control Conference","raw_type":"proceedings-article"},{"id":"pmh:oai:escidoc.org:escidoc:2072770","is_oa":false,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-0024-3EDC-6","pdf_url":null,"source":{"id":"https://openalex.org/S7407052962","display_name":"Max Planck Digital Library","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.75,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W2010258171","https://openalex.org/W2030634628","https://openalex.org/W2056409570","https://openalex.org/W2063326364","https://openalex.org/W2067090991","https://openalex.org/W2084586390","https://openalex.org/W2110837625","https://openalex.org/W2171842311","https://openalex.org/W3194182243","https://openalex.org/W4292872153","https://openalex.org/W6666164454"],"related_works":["https://openalex.org/W4255837520","https://openalex.org/W2387011115","https://openalex.org/W4234808182","https://openalex.org/W2382043075","https://openalex.org/W2809151339","https://openalex.org/W2360673138","https://openalex.org/W2809370583","https://openalex.org/W2333722679","https://openalex.org/W4255628145","https://openalex.org/W2093320919"],"abstract_inverted_index":{"This":[0],"article":[1],"deals":[2],"with":[3,52],"a":[4,36,57],"new":[5],"approach":[6],"to":[7,26,54],"stabilizing":[8,58],"boundary":[9],"control":[10,59],"for":[11],"nonlinear":[12],"parabolic":[13],"PDEs.":[14],"The":[15],"system":[16,29],"under":[17],"investigation":[18],"is":[19,42],"the":[20,33,40,45],"quadratic":[21],"heat":[22],"equation.":[23],"In":[24],"order":[25],"stabilize":[27],"this":[28,31],"in":[30],"contribution":[32],"use":[34],"of":[35],"generalized":[37],"distance":[38],"measure,":[39],"discrepancy,":[41],"proposed.":[43],"Applying,":[44],"associated":[46],"stability":[47,50],"theory,":[48],"i.e.":[49],"theory":[51],"respect":[53],"two":[55],"discrepancies,":[56],"law":[60],"can":[61],"be":[62],"derived.":[63]},"counts_by_year":[],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}