{"id":"https://openalex.org/W2981443388","doi":"https://doi.org/10.1137/18m1221448","title":"Carleman Estimates of Some Stochastic Degenerate Parabolic Equations and Application","display_name":"Carleman Estimates of Some Stochastic Degenerate Parabolic Equations and Application","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2981443388","doi":"https://doi.org/10.1137/18m1221448","mag":"2981443388"},"language":"en","primary_location":{"id":"doi:10.1137/18m1221448","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1221448","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/A5100331713","display_name":"Xu Liu","orcid":"https://orcid.org/0000-0002-8984-5485"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Xu Liu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5033247869","display_name":"Yongyi Yu","orcid":"https://orcid.org/0009-0005-7841-3424"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yongyi Yu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100331713"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0054,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.88189792,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"57","issue":"5","first_page":"3527","last_page":"3552"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9994000196456909,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9987000226974487,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.996999979019165,"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/mathematics","display_name":"Mathematics","score":0.8858823776245117},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.8261824250221252},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.7087423801422119},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.6324816942214966},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.6198790073394775},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5593453049659729},{"id":"https://openalex.org/keywords/heat-equation","display_name":"Heat equation","score":0.4858262538909912},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.47627967596054077},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.41773974895477295},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4156229794025421},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.235680490732193},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14793536067008972}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8858823776245117},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.8261824250221252},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.7087423801422119},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.6324816942214966},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.6198790073394775},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5593453049659729},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.4858262538909912},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.47627967596054077},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41773974895477295},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4156229794025421},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.235680490732193},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14793536067008972},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/18m1221448","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1221448","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/G8228992929","display_name":null,"funder_award_id":"11871142","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W260820322","https://openalex.org/W1571469964","https://openalex.org/W1983342414","https://openalex.org/W1989603443","https://openalex.org/W1997406628","https://openalex.org/W2004690811","https://openalex.org/W2009127884","https://openalex.org/W2009386374","https://openalex.org/W2024081271","https://openalex.org/W2057846825","https://openalex.org/W2058901392","https://openalex.org/W2059855094","https://openalex.org/W2069129680","https://openalex.org/W2074891065","https://openalex.org/W2082322823","https://openalex.org/W2083096684","https://openalex.org/W2084599003","https://openalex.org/W2092323644","https://openalex.org/W2096818010","https://openalex.org/W2109347966","https://openalex.org/W2312726706","https://openalex.org/W2585502697","https://openalex.org/W2963624538","https://openalex.org/W2963779061","https://openalex.org/W3102103414"],"related_works":["https://openalex.org/W2971099291","https://openalex.org/W3099211396","https://openalex.org/W2076262709","https://openalex.org/W2040259912","https://openalex.org/W2886810076","https://openalex.org/W2941405134","https://openalex.org/W1484269119","https://openalex.org/W126524403","https://openalex.org/W2009708810","https://openalex.org/W1998200790"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,38,64,117],"devoted":[3],"to":[4,92,94],"establishing":[5],"global":[6],"Carleman":[7,20],"estimates":[8,21],"for":[9,22,66,80],"some":[10],"forward":[11,24,83],"and":[12,33,84],"backward":[13,86],"stochastic":[14,43],"degenerate":[15,55],"parabolic":[16,45],"equations.":[17,106],"First,":[18],"two":[19],"the":[23,54,58,62,70,82,85,105],"equation":[25],"are":[26,90],"derived":[27],"by":[28],"a":[29,95],"weighted":[30,59],"identity":[31,60],"method":[32],"duality":[34],"technique,":[35],"respectively.":[36],"It":[37],"found":[39],"that":[40],"different":[41],"from":[42],"uniformly":[44],"equations,":[46,87],"both":[47,81],"methods":[48],"have":[49],"their":[50],"own":[51],"advantages":[52],"in":[53],"case.":[56],"By":[57,69],"method,":[61],"estimate":[63],"finer":[65],"diffusion":[67],"terms.":[68],"latter,":[71],"regularity":[72],"requirements":[73],"on":[74],"them":[75],"may":[76],"be":[77],"reduced.":[78],"Also,":[79],"drift":[88],"terms":[89],"allowed":[91],"belong":[93],"Sobolev":[96],"space":[97],"of":[98,104,110],"negative":[99],"order,":[100],"which":[101],"guarantees":[102],"well-posedness":[103],"As":[107],"an":[108,113],"application":[109],"these":[111],"estimates,":[112],"insensitizing":[114],"control":[115],"problem":[116],"studied.":[118]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-04T08:04:53.788161","created_date":"2025-10-10T00:00:00"}