{"id":"https://openalex.org/W4380887317","doi":"https://doi.org/10.1137/22m1499698","title":"Improving the Convergence Rates for the Kinetic Fokker\u2013Planck Equation by Optimal Control","display_name":"Improving the Convergence Rates for the Kinetic Fokker\u2013Planck Equation by Optimal Control","publication_year":2023,"publication_date":"2023-06-16","ids":{"openalex":"https://openalex.org/W4380887317","doi":"https://doi.org/10.1137/22m1499698"},"language":"en","primary_location":{"id":"doi:10.1137/22m1499698","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1499698","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/A5008879804","display_name":"Tobias Breiten","orcid":"https://orcid.org/0000-0002-9815-4897"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Tobias Breiten","raw_affiliation_strings":["Institute of Mathematics, Technische Universit\u00e4t Berlin, 10623 Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0002-9815-4897","affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Technische Universit\u00e4t Berlin, 10623 Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074607617","display_name":"Karl Kunisch","orcid":"https://orcid.org/0000-0003-1113-7355"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]},{"id":"https://openalex.org/I4210158379","display_name":"Johann Radon Institute for Computational and Applied Mathematics","ror":"https://ror.org/05a94k872","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I4210158379"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Karl K. Kunisch","raw_affiliation_strings":["Johann Radon Institute for Computational and Applied Mathematics, 4040 Linz, Austria, and Institute of Mathematics, University of Graz, 8010 Graz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johann Radon Institute for Computational and Applied Mathematics, 4040 Linz, Austria, and Institute of Mathematics, University of Graz, 8010 Graz, Austria","institution_ids":["https://openalex.org/I4210158379","https://openalex.org/I4092182"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5008879804"],"corresponding_institution_ids":["https://openalex.org/I4577782"],"apc_list":null,"apc_paid":null,"fwci":0.4839,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.59619141,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"61","issue":"3","first_page":"1557","last_page":"1581"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9954000115394592,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7777040004730225},{"id":"https://openalex.org/keywords/fokker\u2013planck-equation","display_name":"Fokker\u2013Planck equation","score":0.7555767297744751},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6789196729660034},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.6261869072914124},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.5664539933204651},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.5404585003852844},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4974069893360138},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46567413210868835},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.451302170753479},{"id":"https://openalex.org/keywords/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.44915008544921875},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3626268208026886},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.35421860218048096},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2613528370857239}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7777040004730225},{"id":"https://openalex.org/C69123182","wikidata":"https://www.wikidata.org/wiki/Q891766","display_name":"Fokker\u2013Planck equation","level":3,"score":0.7555767297744751},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6789196729660034},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.6261869072914124},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.5664539933204651},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.5404585003852844},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4974069893360138},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46567413210868835},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.451302170753479},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.44915008544921875},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3626268208026886},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.35421860218048096},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2613528370857239},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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":1,"locations":[{"id":"doi:10.1137/22m1499698","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1499698","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":[{"id":"https://openalex.org/G8531514113","display_name":null,"funder_award_id":"EF4-6","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W317158654","https://openalex.org/W1527296550","https://openalex.org/W1538686203","https://openalex.org/W1805381866","https://openalex.org/W1967967021","https://openalex.org/W1974921909","https://openalex.org/W1977657887","https://openalex.org/W2021268474","https://openalex.org/W2026905679","https://openalex.org/W2035353740","https://openalex.org/W2037025184","https://openalex.org/W2082070870","https://openalex.org/W2090385746","https://openalex.org/W2096953755","https://openalex.org/W2096987252","https://openalex.org/W2102329484","https://openalex.org/W2123046091","https://openalex.org/W2133627030","https://openalex.org/W2139558429","https://openalex.org/W2343546005","https://openalex.org/W2401363764","https://openalex.org/W2625797859","https://openalex.org/W2962801599","https://openalex.org/W3103101978","https://openalex.org/W3135106390","https://openalex.org/W3142080596","https://openalex.org/W4240788980","https://openalex.org/W4241092880","https://openalex.org/W4299150230","https://openalex.org/W4300374450"],"related_works":["https://openalex.org/W2005019312","https://openalex.org/W2105459831","https://openalex.org/W1546579375","https://openalex.org/W2127238600","https://openalex.org/W1563296412","https://openalex.org/W16457797","https://openalex.org/W2792258377","https://openalex.org/W1530596433","https://openalex.org/W2096105566","https://openalex.org/W1993854306"],"abstract_inverted_index":{"The":[0,99],"long":[1],"time":[2],"behavior":[3],"and":[4,130],"detailed":[5],"convergence":[6],"analysis":[7],"of":[8,23,28,38,43,55,87,101,129,132],"Langevin":[9],"equations":[10],"have":[11],"received":[12],"increased":[13],"attention":[14],"in":[15],"recent":[16],"years.":[17],"Difficulties":[18],"arise":[19],"from":[20],"a":[21,36,44,96,133,146,151],"lack":[22],"coercivity,":[24],"usually":[25],"termed":[26],"hypocoercivity,":[27],"the":[29,39,53,57,62,102,125,136,156],"underlying":[30,103],"kinetic":[31],"Fokker\u2013Planck":[32],"operator,":[33],"which":[34],"is":[35,66,92,105],"consequence":[37],"partially":[40],"deterministic":[41],"nature":[42],"second":[45],"order":[46],"stochastic":[47],"differential":[48],"equation.":[49],"In":[50],"this":[51],"manuscript,":[52],"effect":[54],"controlling":[56],"confinement":[58],"potential":[59],"without":[60],"altering":[61],"original":[63],"invariant":[64],"measure":[65],"investigated.":[67],"This":[68],"leads":[69],"to":[70,94,108,135],"an":[71,77,88,110,116],"abstract":[72],"bilinear":[73],"control":[74,82,113,138],"system":[75],"with":[76],"unbounded":[78],"but":[79],"infinite-time":[80],"admissible":[81],"operator":[83],"which,":[84],"by":[85],"means":[86],"artificial":[89],"diffusion":[90],"approach,":[91],"shown":[93],"possess":[95],"unique":[97],"solution.":[98],"compactness":[100],"semigroup":[104],"further":[106],"used":[107],"define":[109],"infinite-horizon":[111],"optimal":[112,137],"problem":[114,139],"on":[115,124,145,150],"appropriately":[117],"reduced":[118],"state":[119],"space.":[120],"Under":[121],"smallness":[122],"assumptions":[123],"initial":[126],"data,":[127],"feasibility":[128],"existence":[131],"solution":[134],"are":[140],"discussed.":[141],"Numerical":[142],"results":[143],"based":[144,149],"local":[147],"approximation":[148],"shifted":[152],"Riccati":[153],"equation":[154],"illustrate":[155],"theoretical":[157],"findings.":[158]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}