{"id":"https://openalex.org/W7214277494","doi":"https://doi.org/10.48550/arxiv.2609.29008","title":"Null controllability on measurable sets for the complex cubic Ginzburg--Landau equation","display_name":"Null controllability on measurable sets for the complex cubic Ginzburg--Landau equation","publication_year":2026,"publication_date":"2026-09-24","ids":{"openalex":"https://openalex.org/W7214277494","doi":"https://doi.org/10.48550/arxiv.2609.29008"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.29008","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29008","pdf_url":"https://arxiv.org/pdf/2609.29008","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/2609.29008","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152775524","display_name":"Yu Xiao","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiao, Yu","raw_affiliation_strings":["School of Mathematics and Statistics , Wuhan University , Wuhan 430072 , P.R.China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Wuhan University , Wuhan 430072 , P.R.China","institution_ids":["https://openalex.org/I37461747"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5152933783","display_name":"Can Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhang, Can","raw_affiliation_strings":["School of Mathematics and Statistics , Wuhan University , Wuhan 430072 , P.R.China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Wuhan University , Wuhan 430072 , P.R.China","institution_ids":["https://openalex.org/I37461747"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I37461747"],"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.0003000000142492354,"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"}},{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/null-controllability","display_name":"null controllability","score":1.0},{"id":"https://openalex.org/keywords/nonlinear-parabolic-equations","display_name":"nonlinear parabolic equations","score":0.9129999876022339},{"id":"https://openalex.org/keywords/local-null-controllability","display_name":"local null controllability","score":0.6990000009536743}],"concepts":[{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.8888000249862671},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8086000084877014},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6003999710083008},{"id":"https://openalex.org/C203763787","wikidata":"https://www.wikidata.org/wiki/Q371029","display_name":"Null (SQL)","level":2,"score":0.5939000248908997},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5483999848365784},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.44179999828338623},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.4334999918937683},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.429500013589859},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3874000012874603},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3741999864578247},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3707999885082245},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.3625999987125397},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.3619999885559082},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3418000042438507},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.3140000104904175},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.30079999566078186},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28859999775886536},{"id":"https://openalex.org/C43994743","wikidata":"https://www.wikidata.org/wiki/Q516776","display_name":"Measurable function","level":3,"score":0.2867000102996826},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2768000066280365},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.27480000257492065},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.2736000120639801},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2678000032901764},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.26339998841285706},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.2606000006198883},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.257999986410141},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.25459998846054077},{"id":"https://openalex.org/C2780799671","wikidata":"https://www.wikidata.org/wiki/Q17087362","display_name":"Transient (computer programming)","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.29008","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29008","pdf_url":"https://arxiv.org/pdf/2609.29008","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.2609.29008","doi":"https://doi.org/10.48550/arxiv.2609.29008","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.29008","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:2609.29008","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29008","pdf_url":"https://arxiv.org/pdf/2609.29008","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/G7949349594","display_name":null,"funder_award_id":"12422118","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/W7214277494.pdf","grobid_xml":"https://content.openalex.org/works/W7214277494.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W7154008210","https://openalex.org/W7154624478","https://openalex.org/W7161685041","https://openalex.org/W7164031422","https://openalex.org/W7167573599"],"related_works":["https://openalex.org/W4411213131","https://openalex.org/W2588132219","https://openalex.org/W2086758045","https://openalex.org/W2949258032","https://openalex.org/W2090929933","https://openalex.org/W1988999521","https://openalex.org/W3207333376","https://openalex.org/W2094786792","https://openalex.org/W2557540798","https://openalex.org/W4403445296"],"abstract_inverted_index":{"This":[0,40,115],"paper":[1],"investigates":[2],"the":[3,7,46,50,69,74,97,103,107,111,121],"null":[4,123],"controllability":[5,124],"of":[6,35,64],"complex":[8],"cubic":[9],"Ginzburg--Landau":[10],"equation":[11],"with":[12,88],"controls":[13],"supported":[14],"on":[15,45,72,125],"general":[16],"space-time":[17],"measurable":[18,126],"sets.":[19],"Starting":[20],"from":[21],"a":[22,28,62,78,85,117],"positive-measure":[23],"control":[24,127],"set,":[25],"we":[26],"use":[27],"slicing":[29],"argument":[30,60],"to":[31,120],"obtain":[32],"time":[33],"slices":[34],"uniformly":[36],"positive":[37,80],"spatial":[38],"measure.":[39],"yields":[41],"uniform":[42,79],"spectral":[43],"inequalities":[44],"slices,":[47],"which":[48,73],"are":[49],"key":[51],"ingredient":[52],"in":[53],"constructing":[54],"quantitative":[55],"stabilizing":[56],"feedbacks.":[57],"A":[58],"density-point":[59],"provides":[61,116],"sequence":[63],"shrinking":[65],"intervals":[66],"accumulating":[67],"at":[68,110],"density":[70,113],"point,":[71],"active":[75],"times":[76],"have":[77],"density.":[81],"We":[82],"then":[83],"apply":[84],"time-iteration":[86],"scheme":[87],"piecewise":[89],"feedback":[90],"laws":[91],"and":[92],"increasing":[93],"decay":[94],"rates.":[95],"Iterating":[96],"resulting":[98],"stabilization":[99],"estimates":[100],"shows":[101],"that":[102],"closed-loop":[104],"solution":[105],"reaches":[106],"zero":[108],"state":[109],"selected":[112],"point.":[114],"constructive":[118],"approach":[119],"local":[122],"sets":[128],"for":[129],"nonlinear":[130],"parabolic":[131],"equations.":[132]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-26T00:00:00"}
