{"id":"https://openalex.org/W7214324497","doi":"https://doi.org/10.48550/arxiv.2609.28937","title":"Null Controllability of a Stochastic Parabolic Equation with a Space-Dependent Analytic Noise Coefficient","display_name":"Null Controllability of a Stochastic Parabolic Equation with a Space-Dependent Analytic Noise Coefficient","publication_year":2026,"publication_date":"2026-09-24","ids":{"openalex":"https://openalex.org/W7214324497","doi":"https://doi.org/10.48550/arxiv.2609.28937"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.28937","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.28937","pdf_url":"https://arxiv.org/pdf/2609.28937","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.28937","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152774474","display_name":"Qi L\u00fc","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"L\u00fc, Qi","raw_affiliation_strings":["School of Mathematics , Sichuan University , Chengdu 610064 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , Sichuan University , Chengdu 610064 , China","institution_ids":["https://openalex.org/I24185976"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5159983769","display_name":"Yu Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4800084","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693","country_code":"CN","type":"education","lineage":["https://openalex.org/I4800084"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wang, Yu","raw_affiliation_strings":["School of Mathematics , Southwest Jiaotong University , Chengdu 611756 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , Southwest Jiaotong University , Chengdu 611756 , China","institution_ids":["https://openalex.org/I4800084"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"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":0.9994999766349792,"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":0.9994999766349792,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":9.999999747378752e-05,"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/null-controllability","display_name":"null controllability","score":0.9879999756813049},{"id":"https://openalex.org/keywords/parabolic-stochastic-partial-differential-equations","display_name":"parabolic stochastic partial differential equations","score":0.9449999928474426},{"id":"https://openalex.org/keywords/multiplicative-noise","display_name":"multiplicative noise","score":0.7630000114440918},{"id":"https://openalex.org/keywords/drift-control","display_name":"drift control","score":0.8550000190734863},{"id":"https://openalex.org/keywords/observability-inequality","display_name":"observability inequality","score":0.8550000190734863},{"id":"https://openalex.org/keywords/approximate-controllability","display_name":"approximate controllability","score":0.9150000214576721},{"id":"https://openalex.org/keywords/flat-torus","display_name":"flat torus","score":0.7110000252723694}],"concepts":[{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.8312000036239624},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.817799985408783},{"id":"https://openalex.org/C75413324","wikidata":"https://www.wikidata.org/wiki/Q1530791","display_name":"Square-integrable function","level":2,"score":0.6897000074386597},{"id":"https://openalex.org/C36299963","wikidata":"https://www.wikidata.org/wiki/Q1369844","display_name":"Observability","level":2,"score":0.661899983882904},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6013000011444092},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5232999920845032},{"id":"https://openalex.org/C203763787","wikidata":"https://www.wikidata.org/wiki/Q371029","display_name":"Null (SQL)","level":2,"score":0.4108999967575073},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.3919999897480011},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.38989999890327454},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.3788999915122986},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3594000041484833},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.34049999713897705},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.33820000290870667},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.3075000047683716},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.2992999851703644},{"id":"https://openalex.org/C42357961","wikidata":"https://www.wikidata.org/wiki/Q213363","display_name":"Open set","level":2,"score":0.2912999987602234},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.2854999899864197},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.2824999988079071},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.2547000050544739},{"id":"https://openalex.org/C157709441","wikidata":"https://www.wikidata.org/wiki/Q1411887","display_name":"Uniform convergence","level":3,"score":0.2538999915122986},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.28937","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.28937","pdf_url":"https://arxiv.org/pdf/2609.28937","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2609.28937","doi":"https://doi.org/10.48550/arxiv.2609.28937","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.28937","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.28937","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.28937","pdf_url":"https://arxiv.org/pdf/2609.28937","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G6963497035","display_name":null,"funder_award_id":"12025105","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7804536706","display_name":null,"funder_award_id":"12401589","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214324497.pdf","grobid_xml":"https://content.openalex.org/works/W7214324497.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3178150710","https://openalex.org/W4390306499","https://openalex.org/W2142238846","https://openalex.org/W2061278786","https://openalex.org/W4411103183","https://openalex.org/W7117295583","https://openalex.org/W4405963476","https://openalex.org/W2744875607","https://openalex.org/W4394770225","https://openalex.org/W4409768551"],"abstract_inverted_index":{"We":[0,72],"consider":[1],"a":[2,48,74,121,136],"stochastic":[3],"parabolic":[4],"equation":[5],"on":[6,31,120],"the":[7,20,32,55,127],"$n$-dimensional":[8],"flat":[9],"torus":[10],"$\\mathbb{T}^n=(\\mathbb{R}/(2\u03c0\\mathbb":[11],"Z))^n$,":[12],"$n\\in\\mathbb":[13],"N$,":[14],"whose":[15],"only":[16,60],"control":[17],"acts":[18],"in":[19,66],"drift.":[21],"The":[22,101,116],"multiplicative-noise":[23],"coefficient":[24],"is":[25,59,118],"adapted":[26,98],"and":[27,36,84,135],"may":[28],"depend":[29],"jointly":[30],"sample":[33,70],"point,":[34],"time,":[35,67],"space.":[37],"Its":[38],"spatial":[39,91],"profiles":[40],"are":[41],"assumed":[42],"to":[43,62,110],"be":[44,63],"real":[45],"analytic":[46,57,123],"with":[47,78],"uniform":[49],"positive":[50,94],"radius":[51],"of":[52,93,133],"analyticity,":[53],"while":[54],"corresponding":[56],"norm":[58,83],"required":[61],"square":[64],"integrable":[65],"uniformly":[68],"along":[69],"paths.":[71],"prove":[73],"state-only":[75],"observability":[76],"inequality":[77],"an":[79],"$L^1$-in-time":[80],"mean-square":[81],"observation":[82],"deduce":[85],"null":[86],"controllability":[87,109],"from":[88],"every":[89],"measurable":[90],"set":[92],"measure":[95],"by":[96,131],"one":[97],"drift":[99],"control.":[100],"same":[102],"one-time":[103],"interpolation":[104],"estimate":[105,125],"also":[106],"yields":[107],"approximate":[108],"arbitrary":[111],"square-integrable":[112],"random":[113],"terminal":[114],"targets.":[115],"proof":[117],"based":[119],"direct":[122],"energy":[124],"for":[126],"adjoint":[128],"state,":[129],"followed":[130],"propagation":[132],"smallness":[134],"telescoping":[137],"argument.":[138]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-26T00:00:00"}
