{"id":"https://openalex.org/W2048489411","doi":"https://doi.org/10.1137/050645944","title":"Nonlinear Diffusion Governed by McKean\u2013Vlasov Equation on Hilbert Space and Optimal Control","display_name":"Nonlinear Diffusion Governed by McKean\u2013Vlasov Equation on Hilbert Space and Optimal Control","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2048489411","doi":"https://doi.org/10.1137/050645944","mag":"2048489411"},"language":"en","primary_location":{"id":"doi:10.1137/050645944","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050645944","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":"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/A5103039267","display_name":"Naveed Ahmed","orcid":"https://orcid.org/0000-0002-9322-0373"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"N. U. Ahmed","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5103039267"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.07623631,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"46","issue":"1","first_page":"356","last_page":"378"},"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":0.9997000098228455,"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":0.9997000098228455,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.995199978351593,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8628736734390259},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7662696838378906},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.7035080790519714},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6527344584465027},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6041975617408752},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.6013681292533875},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5490661859512329},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5224534273147583},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4719994068145752},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4633078873157501},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.462547242641449},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.43213266134262085},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.30384498834609985},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09152612090110779}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8628736734390259},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7662696838378906},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.7035080790519714},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6527344584465027},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6041975617408752},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.6013681292533875},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5490661859512329},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5224534273147583},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4719994068145752},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4633078873157501},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.462547242641449},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.43213266134262085},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.30384498834609985},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09152612090110779},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/050645944","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050645944","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1514451635","https://openalex.org/W1973827783","https://openalex.org/W1974345218","https://openalex.org/W1976901000","https://openalex.org/W2002020306","https://openalex.org/W2032164161","https://openalex.org/W2048341005","https://openalex.org/W2065172718","https://openalex.org/W2078076766"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W4301247218","https://openalex.org/W2129818458","https://openalex.org/W4243074410","https://openalex.org/W4289551052","https://openalex.org/W4390756076","https://openalex.org/W2969742028"],"abstract_inverted_index":{"This":[0],"paper":[1],"deals":[2],"with":[3,35,62],"optimal":[4,75],"feedback":[5,32],"control":[6,60],"of":[7,10,18,24,31,46,68,74],"measure\u2010valued":[8,25],"solutions":[9,26],"nonlinear":[11],"diffusion":[12],"governed":[13],"by":[14],"McKean\u2013Vlasov":[15],"equations.":[16],"Questions":[17],"existence,":[19],"uniqueness,":[20],"and":[21,41,70],"regularity":[22],"properties":[23,45],"are":[27,54,66],"addressed.":[28],"A":[29],"class":[30],"controls":[33,53],"furnished":[34],"a":[36],"weak":[37],"topology":[38],"is":[39],"introduced,":[40],"some":[42],"important":[43],"topological":[44],"the":[47,72],"attainable":[48],"set":[49],"corresponding":[50],"to":[51],"these":[52],"presented.":[55],"We":[56],"consider":[57],"several":[58],"typical":[59],"problems":[61],"objective":[63],"functionals":[64],"which":[65],"functions":[67],"measures":[69],"prove":[71],"existence":[73],"controls.":[76]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}