{"id":"https://openalex.org/W7214917500","doi":"https://doi.org/10.48550/arxiv.2609.36204","title":"Unique continuation for the periodic Benjamin-Bona-Mahony equation","display_name":"Unique continuation for the periodic Benjamin-Bona-Mahony equation","publication_year":2026,"publication_date":"2026-09-28","ids":{"openalex":"https://openalex.org/W7214917500","doi":"https://doi.org/10.48550/arxiv.2609.36204"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.36204","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36204","pdf_url":"https://arxiv.org/pdf/2609.36204","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/2609.36204","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5123236857","display_name":"Roberto de A. Capistrano-Filho","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I25112270","display_name":"Universidade Federal de Pernambuco","ror":"https://ror.org/047908t24","country_code":"BR","type":"education","lineage":["https://openalex.org/I25112270"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Filho, Roberto de A. Capistrano","raw_affiliation_strings":["UFPE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UFPE","institution_ids":["https://openalex.org/I25112270"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018885109","display_name":"V. M. Martinez Alvarez","orcid":"https://orcid.org/0000-0002-0070-9883","observed_orcids":["https://orcid.org/0000-0002-0070-9883"]},"institutions":[{"id":"https://openalex.org/I25112270","display_name":"Universidade Federal de Pernambuco","ror":"https://ror.org/047908t24","country_code":"BR","type":"education","lineage":["https://openalex.org/I25112270"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Martinez, Victor Hugo Gonzalez","raw_affiliation_strings":["UFPE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UFPE","institution_ids":["https://openalex.org/I25112270"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5153652565","display_name":"Ailton Campos do Nascimento","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I3121799822","display_name":"Universidade Federal do Piau\u00ed","ror":"https://ror.org/00kwnx126","country_code":"BR","type":"education","lineage":["https://openalex.org/I3121799822"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Nascimento, Ailton Campos do","raw_affiliation_strings":["UFPI"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UFPI","institution_ids":["https://openalex.org/I3121799822"]}]}],"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":0.5023999810218811,"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":0.5023999810218811,"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":0.46480000019073486,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.024299999698996544,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/unique-continuation","display_name":"unique continuation","score":0.9710000157356262},{"id":"https://openalex.org/keywords/energy-space","display_name":"energy space","score":0.5889999866485596},{"id":"https://openalex.org/keywords/boundary-feedback","display_name":"boundary feedback","score":0.8169999718666077},{"id":"https://openalex.org/keywords/linearized-equations","display_name":"linearized equations","score":0.7990000247955322},{"id":"https://openalex.org/keywords/generating-series","display_name":"generating series","score":0.5910000205039978},{"id":"https://openalex.org/keywords/nonlinear-dispersive-equations","display_name":"nonlinear dispersive equations","score":0.5899999737739563}],"concepts":[{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.8592000007629395},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7968999743461609},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5967000126838684},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5791000127792358},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5440999865531921},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.47429999709129333},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.42800000309944153},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4221000075340271},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.39649999141693115},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3939000070095062},{"id":"https://openalex.org/C2779844894","wikidata":"https://www.wikidata.org/wiki/Q5421516","display_name":"Exponential dichotomy","level":3,"score":0.35190001130104065},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.33329999446868896},{"id":"https://openalex.org/C110342517","wikidata":"https://www.wikidata.org/wiki/Q1129902","display_name":"Constant coefficients","level":2,"score":0.3278999924659729},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.31869998574256897},{"id":"https://openalex.org/C3018651601","wikidata":"https://www.wikidata.org/wiki/Q183635","display_name":"Feedback control","level":2,"score":0.28119999170303345},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.27149999141693115},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.27079999446868896},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.258899986743927},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.2540000081062317},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.25369998812675476}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.36204","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36204","pdf_url":"https://arxiv.org/pdf/2609.36204","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.2609.36204","doi":"https://doi.org/10.48550/arxiv.2609.36204","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.36204","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.36204","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36204","pdf_url":"https://arxiv.org/pdf/2609.36204","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/G247168254","display_name":null,"funder_award_id":"421573/2023-6","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G3129623590","display_name":null,"funder_award_id":"301744/2025-4","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"}],"funders":[{"id":"https://openalex.org/F4320321091","display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","ror":"https://ror.org/00x0ma614"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320324901","display_name":"Universidade Federal de Pernambuco","ror":"https://ror.org/047908t24"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214917500.pdf","grobid_xml":"https://content.openalex.org/works/W7214917500.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7120470886","https://openalex.org/W2010270143","https://openalex.org/W1590325349","https://openalex.org/W7101043119","https://openalex.org/W2953190449","https://openalex.org/W1990005477","https://openalex.org/W4392214458","https://openalex.org/W2092989727","https://openalex.org/W4226455502","https://openalex.org/W2056560536"],"abstract_inverted_index":{"We":[0,138],"prove":[1],"unique":[2,32,146],"continuation":[3,33,147],"for":[4,53,110,116,122,135,148],"the":[5,11,58,61,74,130,149],"real":[6,103],"periodic":[7],"Benjamin--Bona--Mahony":[8],"equation":[9,151],"in":[10,55,133],"energy":[12],"space:":[13],"a":[14,18,21,93,117,141],"solution":[15,59],"that":[16,26,129],"equals":[17],"constant":[19,27],"on":[20],"nonempty":[22],"space--time":[23],"strip":[24],"is":[25],"everywhere.":[28],"In":[29],"particular,":[30],"Rosier's":[31,107],"conjecture":[34],"[23]":[35],"holds":[36],"without":[37],"any":[38],"smallness":[39],"or":[40],"mean":[41],"assumption.":[42],"It":[43],"even":[44],"suffices":[45],"to":[46,100],"observe,":[47],"at":[48],"one":[49],"point":[50],"$x_0$":[51],"and":[52,60,68,73,97,115,152],"$t$":[54],"an":[56,85],"interval,":[57],"potential":[62],"$\u03c8=(1-\\partial_x^2)^{-1}(u+u^2/2)$":[63],"of":[64,89,144],"its":[65],"flux:":[66],"$u(x_0,t)=C$":[67],"$\u03c8(x_0,t)=C+C^2/2$":[69],"imply":[70],"$u\\equiv":[71],"C$,":[72],"second":[75],"condition":[76],"cannot":[77],"be":[78],"dropped":[79],"when":[80],"$C=-1$.":[81],"The":[82],"proof":[83,143],"uses":[84],"exponentially":[86],"weighted":[87],"Hamiltonian":[88],"indefinite":[90],"sign":[91],"with":[92],"coercive":[94],"dissipation":[95],"identity,":[96],"it":[98],"applies":[99],"every":[101],"nonconstant":[102],"polynomial":[104],"flux.":[105],"Consequently,":[106],"stabilization":[108],"results":[109],"two":[111],"localized":[112],"feedback":[113,119],"laws":[114],"boundary":[118],"hold":[120],"unconditionally,":[121],"arbitrary":[123],"data.":[124],"Stationary":[125],"step":[126],"profiles":[127],"show":[128],"theorem":[131],"fails":[132],"$H^s$":[134],"$0\\leq":[136],"s<1/2$.":[137],"also":[139],"give":[140],"generating-series":[142],"single-point":[145],"linearized":[150],"discuss":[153],"related":[154],"control":[155],"results.":[156]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-01T00:00:00"}