{"id":"https://openalex.org/W7220700152","doi":"https://doi.org/10.48550/arxiv.2610.05704","title":"Observability from Measurable Sets for One-Dimensional Heat Equations with Bounded Spacetime Potentials","display_name":"Observability from Measurable Sets for One-Dimensional Heat Equations with Bounded Spacetime Potentials","publication_year":2026,"publication_date":"2026-10-05","ids":{"openalex":"https://openalex.org/W7220700152","doi":"https://doi.org/10.48550/arxiv.2610.05704"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.05704","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05704","pdf_url":"https://arxiv.org/pdf/2610.05704","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/2610.05704","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5157695710","display_name":"Xiaomin Zhu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I58995867","display_name":"Civil Aviation Flight University of China","ror":"https://ror.org/01xyb1v19","country_code":"CN","type":"education","lineage":["https://openalex.org/I58995867"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhu, Xiaomin","raw_affiliation_strings":["Civil Aviation Flight University of China , Deyang 618307 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Civil Aviation Flight University of China , Deyang 618307 , China","institution_ids":["https://openalex.org/I58995867"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5157695710"],"corresponding_institution_ids":["https://openalex.org/I58995867"],"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":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"}},{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","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/observability","display_name":"observability","score":0.7559999823570251},{"id":"https://openalex.org/keywords/one-dimensional-heat-equation","display_name":"one-dimensional heat equation","score":0.7870000004768372},{"id":"https://openalex.org/keywords/null-controllability","display_name":"null controllability","score":0.9670000076293945},{"id":"https://openalex.org/keywords/exponential-decay-estimates","display_name":"exponential decay estimates","score":0.5180000066757202}],"concepts":[{"id":"https://openalex.org/C36299963","wikidata":"https://www.wikidata.org/wiki/Q1369844","display_name":"Observability","level":2,"score":0.9229999780654907},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.8892999887466431},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6845999956130981},{"id":"https://openalex.org/C130187892","wikidata":"https://www.wikidata.org/wiki/Q133327","display_name":"Spacetime","level":2,"score":0.6182000041007996},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.60589998960495},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5843999981880188},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.5669999718666077},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5264000296592712},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5153999924659729},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.48829999566078186},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4059000015258789},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.36739999055862427},{"id":"https://openalex.org/C203763787","wikidata":"https://www.wikidata.org/wiki/Q371029","display_name":"Null (SQL)","level":2,"score":0.36649999022483826},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.32690000534057617},{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.30480000376701355},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.29660001397132874},{"id":"https://openalex.org/C96402334","wikidata":"https://www.wikidata.org/wiki/Q3030793","display_name":"Space time","level":2,"score":0.2840999960899353},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.2718999981880188},{"id":"https://openalex.org/C41254897","wikidata":"https://www.wikidata.org/wiki/Q1139715","display_name":"Causal sets","level":5,"score":0.2651999890804291},{"id":"https://openalex.org/C110342517","wikidata":"https://www.wikidata.org/wiki/Q1129902","display_name":"Constant coefficients","level":2,"score":0.2639999985694885},{"id":"https://openalex.org/C175454919","wikidata":"https://www.wikidata.org/wiki/Q2342396","display_name":"Bounded operator","level":3,"score":0.2637999951839447}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.05704","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05704","pdf_url":"https://arxiv.org/pdf/2610.05704","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.2610.05704","doi":"https://doi.org/10.48550/arxiv.2610.05704","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.05704","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.05704","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05704","pdf_url":"https://arxiv.org/pdf/2610.05704","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":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220700152.pdf","grobid_xml":"https://content.openalex.org/works/W7220700152.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1973734835","https://openalex.org/W1993046097","https://openalex.org/W2011483362","https://openalex.org/W2018487834","https://openalex.org/W2089937637","https://openalex.org/W2126805081","https://openalex.org/W2625273684","https://openalex.org/W2888785267","https://openalex.org/W2963551263","https://openalex.org/W2963576390","https://openalex.org/W2964171923","https://openalex.org/W2994698012","https://openalex.org/W4393178421","https://openalex.org/W4411946187"],"related_works":["https://openalex.org/W4403667415","https://openalex.org/W6959826850","https://openalex.org/W2984685561","https://openalex.org/W3043278803","https://openalex.org/W4404517665","https://openalex.org/W2979903828","https://openalex.org/W7214330183","https://openalex.org/W2606903949","https://openalex.org/W2908237742","https://openalex.org/W2779271942"],"abstract_inverted_index":{"This":[0],"paper":[1],"study":[2],"observability":[3,26,93],"for":[4,122],"the":[5,80,92,102,105,117,123],"Dirichlet":[6],"heat":[7],"equation":[8],"on":[9,19,89,112],"a":[10,14,44,84],"bounded":[11,16,67,96],"interval":[12],"with":[13,34,43,70,119],"real":[15],"potential":[17],"depending":[18],"space":[20],"and":[21],"time.":[22],"We":[23],"prove":[24],"an":[25],"inequality":[27],"from":[28],"every":[29,76],"measurable":[30],"subset":[31],"of":[32,79,104],"spacetime":[33,51],"positive":[35,50,86],"measure.":[36],"The":[37,107],"constant":[38,94],"is":[39,53,95],"uniform":[40],"over":[41],"potentials":[42],"prescribed":[45],"$L^\\infty$":[46],"bound.":[47],"By":[48],"duality,":[49],"measure":[52],"equivalent":[54],"to":[55,125],"null":[56],"controllability":[57],"by":[58,98,116],"square-integrable":[59],"distributed":[60],"controls.":[61],"Controls":[62],"can":[63],"also":[64],"be":[65],"chosen":[66],"in":[68,72,101],"time":[69],"values":[71],"$L^2$.":[73],"If":[74],"almost":[75],"spatial":[77],"slice":[78],"observation":[81,110],"set":[82],"has":[83],"fixed":[85],"lower":[87],"bound":[88],"its":[90],"measure,":[91],"above":[97],"$C_0e^{C_1/T}$,":[99],"uniformly":[100],"locations":[103],"slices.":[106],"proof":[108],"combines":[109],"estimates":[111,121],"finite-dimensional":[113],"spaces":[114],"transported":[115],"evolution":[118],"decay":[120],"distance":[124],"those":[126],"spaces.":[127]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}