{"id":"https://openalex.org/W3092533768","doi":"https://doi.org/10.1137/20m1372603","title":"A Fredholm Transformation for the Rapid Stabilization of a Degenerate Parabolic Equation","display_name":"A Fredholm Transformation for the Rapid Stabilization of a Degenerate Parabolic Equation","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3092533768","doi":"https://doi.org/10.1137/20m1372603","mag":"3092533768"},"language":"en","primary_location":{"id":"doi:10.1137/20m1372603","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1372603","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2010.05476","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051831147","display_name":"Ludovick Gagnon","orcid":"https://orcid.org/0000-0002-8329-7983"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Ludovick Gagnon","raw_affiliation_strings":["Inria, SPHINX"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inria, SPHINX","institution_ids":["https://openalex.org/I1326498283"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090052586","display_name":"Pierre Lissy","orcid":null},"institutions":[{"id":"https://openalex.org/I56435720","display_name":"Universit\u00e9 Paris Dauphine-PSL","ror":"https://ror.org/052bz7812","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pierre Lissy","raw_affiliation_strings":["Universit\u00e9 Paris Dauphine - PSL"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Paris Dauphine - PSL","institution_ids":["https://openalex.org/I56435720"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043449102","display_name":"Swann Marx","orcid":"https://orcid.org/0000-0002-0722-3560"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Swann Marx","raw_affiliation_strings":["LS2N"],"raw_orcid":"https://orcid.org/0000-0002-0722-3560","affiliations":[{"raw_affiliation_string":"LS2N","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2705,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.5020101,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"59","issue":"5","first_page":"3828","last_page":"3859"},"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":0.9998999834060669,"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":0.9998999834060669,"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":0.9980999827384949,"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":0.9937999844551086,"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/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.8173117637634277},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.7612243890762329},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.730659544467926},{"id":"https://openalex.org/keywords/backstepping","display_name":"Backstepping","score":0.7075367569923401},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6346107721328735},{"id":"https://openalex.org/keywords/fredholm-integral-equation","display_name":"Fredholm integral equation","score":0.6217131614685059},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5667595863342285},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4859870374202728},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.46676915884017944},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.4514540433883667},{"id":"https://openalex.org/keywords/fredholm-theory","display_name":"Fredholm theory","score":0.4403223693370819},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41855695843696594},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3438592553138733},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.33601969480514526},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.21841999888420105},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.18937081098556519},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17912593483924866},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11571064591407776},{"id":"https://openalex.org/keywords/adaptive-control","display_name":"Adaptive control","score":0.0872955322265625}],"concepts":[{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.8173117637634277},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.7612243890762329},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.730659544467926},{"id":"https://openalex.org/C72218879","wikidata":"https://www.wikidata.org/wiki/Q4839759","display_name":"Backstepping","level":4,"score":0.7075367569923401},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6346107721328735},{"id":"https://openalex.org/C89285879","wikidata":"https://www.wikidata.org/wiki/Q2991898","display_name":"Fredholm integral equation","level":3,"score":0.6217131614685059},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5667595863342285},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4859870374202728},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.46676915884017944},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.4514540433883667},{"id":"https://openalex.org/C518188847","wikidata":"https://www.wikidata.org/wiki/Q4455098","display_name":"Fredholm theory","level":4,"score":0.4403223693370819},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41855695843696594},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3438592553138733},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.33601969480514526},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.21841999888420105},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.18937081098556519},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17912593483924866},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11571064591407776},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.0872955322265625},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/20m1372603","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1372603","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2010.05476","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2010.05476","pdf_url":"https://arxiv.org/pdf/2010.05476","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3092533768","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2010.05476.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:HAL:hal-02963160v1","is_oa":false,"landing_page_url":"https://hal.science/hal-02963160","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Control and Optimization, 2021, 59 (5), ⟨10.1137/20M1372603⟩","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:basepub.dauphine.psl.eu:123456789/22312","is_oa":true,"landing_page_url":"https://basepub.dauphine.psl.eu/handle/123456789/22312","pdf_url":null,"source":{"id":"https://openalex.org/S4306401007","display_name":"Base Institutionnelle de Recherche de l'universit\u00e9 Paris-Dauphine (BIRD) (University Paris-Dauphine)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102197404","host_organization_name":"Universit\u00e9 Paris-Sud","host_organization_lineage":["https://openalex.org/I102197404"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article accept\u00e9 pour publication ou publi\u00e9"},{"id":"doi:10.48550/arxiv.2010.05476","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2010.05476","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2010.05476","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2010.05476","pdf_url":"https://arxiv.org/pdf/2010.05476","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"score":0.8999999761581421,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G521015467","display_name":"Observer Design for Infinite dimensional SyStEm","funder_award_id":"ANR-19-CE48-0004","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6044510825","display_name":null,"funder_award_id":"ANR-19-CE48-0004-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320327974","display_name":"Conseil R\u00e9gional des Pays de la Loire","ror":null},{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1582892423","https://openalex.org/W1587708275","https://openalex.org/W1618634548","https://openalex.org/W1729520098","https://openalex.org/W1964857679","https://openalex.org/W1977835435","https://openalex.org/W2002744405","https://openalex.org/W2025447499","https://openalex.org/W2043585825","https://openalex.org/W2052810255","https://openalex.org/W2066096538","https://openalex.org/W2074126996","https://openalex.org/W2074462890","https://openalex.org/W2081338783","https://openalex.org/W2114920878","https://openalex.org/W2135778954","https://openalex.org/W2333341447","https://openalex.org/W2478537913","https://openalex.org/W2563249773","https://openalex.org/W2592178514","https://openalex.org/W2610818604","https://openalex.org/W2910287291","https://openalex.org/W2963588029","https://openalex.org/W2963867035","https://openalex.org/W2964292842"],"related_works":["https://openalex.org/W2580519087","https://openalex.org/W1988895947","https://openalex.org/W2945319509","https://openalex.org/W2755184962","https://openalex.org/W2964918925","https://openalex.org/W2499617466","https://openalex.org/W2013781383","https://openalex.org/W2094015961","https://openalex.org/W3128019838","https://openalex.org/W1520594255","https://openalex.org/W2793524140","https://openalex.org/W1858469755","https://openalex.org/W3025194014","https://openalex.org/W2597804013","https://openalex.org/W2221987248","https://openalex.org/W78099240","https://openalex.org/W2056026261","https://openalex.org/W2735525108","https://openalex.org/W1985415800","https://openalex.org/W3094227663"],"abstract_inverted_index":{"This":[0],"paper":[1,61,80],"deals":[2],"with":[3,12],"the":[4,33,79,85,94,103],"rapid":[5,104],"stabilization":[6],"of":[7,78],"a":[8,13,22,66],"degenerate":[9,34],"parabolic":[10,35],"equation":[11,36],"right":[14],"Dirich-let":[15],"control.":[16],"Our":[17],"strategy":[18],"consists":[19],"in":[20,59,93],"applying":[21],"backstepping":[23],"strategy,":[24],"which":[25],"seeks":[26],"to":[27,37,82,101],"find":[28],"an":[29,40],"invertible":[30,92],"transformation":[31,56,87],"mapping":[32],"stabilize":[38],"into":[39],"exponentially":[41],"stable":[42],"system":[43],"whose":[44],"decay":[45],"rate":[46],"is":[47,62,81,88],"known":[48],"and":[49,91],"as":[50,52],"large":[51],"we":[53],"desire.":[54],"The":[55,75],"under":[57],"consideration":[58],"this":[60],"Fredholm.":[63],"It":[64,98],"involves":[65],"kernel":[67],"solving":[68],"itself":[69],"another":[70],"PDE,":[71],"at":[72],"least":[73],"formally.":[74],"main":[76],"goal":[77],"prove":[83],"that":[84],"Fredholm":[86],"well-defined,":[89],"continuous":[90],"natural":[95],"energy":[96],"space.":[97],"allows":[99],"us":[100],"deduce":[102],"stabilization.":[105]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2025-10-10T00:00:00"}