{"id":"https://openalex.org/W4382402166","doi":"https://doi.org/10.3390/math11132881","title":"The Problem of Boundary Control of the Thermal Process in a Rod","display_name":"The Problem of Boundary Control of the Thermal Process in a Rod","publication_year":2023,"publication_date":"2023-06-27","ids":{"openalex":"https://openalex.org/W4382402166","doi":"https://doi.org/10.3390/math11132881"},"language":"en","primary_location":{"id":"doi:10.3390/math11132881","doi":"https://doi.org/10.3390/math11132881","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math11132881","pdf_url":"https://www.mdpi.com/2227-7390/11/13/2881/pdf?version=1687860875","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W4382402166"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2227-7390/11/13/2881/pdf?version=1687860875","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013018095","display_name":"Vanya Rafayelovich Barseghyan","orcid":"https://orcid.org/0000-0001-6518-3694","observed_orcids":["https://orcid.org/0000-0001-6518-3694"]},"institutions":[{"id":"https://openalex.org/I196551433","display_name":"Yerevan State University","ror":"https://ror.org/00s8vne50","country_code":"AM","type":"education","lineage":["https://openalex.org/I196551433"]},{"id":"https://openalex.org/I99064381","display_name":"National Academy of Sciences of Armenia","ror":"https://ror.org/04mczx267","country_code":"AM","type":"government","lineage":["https://openalex.org/I99064381"]}],"countries":["AM"],"is_corresponding":false,"raw_author_name":"Vanya Barseghyan","raw_affiliation_strings":["Institute of Mechanics, The National Academy of Sciences of the Republic of Armenia, Yerevan State University, Yerevan 0019, Armenia"],"raw_orcid":"https://orcid.org/0000-0001-6518-3694","affiliations":[{"raw_affiliation_string":"Institute of Mechanics, The National Academy of Sciences of the Republic of Armenia, Yerevan State University, Yerevan 0019, Armenia","institution_ids":["https://openalex.org/I196551433","https://openalex.org/I99064381"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090692957","display_name":"\u0421\u043e\u043b\u043e\u0434\u0443\u0448\u0430 \u0421\u0432\u0435\u0442\u043b\u0430\u043d\u0430 \u0412\u0438\u0442\u0430\u043b\u044c\u0435\u0432\u043d\u0430","orcid":"https://orcid.org/0000-0001-6162-7542","observed_orcids":["https://orcid.org/0000-0001-6162-7542"]},"institutions":[{"id":"https://openalex.org/I4210114158","display_name":"Melentiev Energy Systems Institute","ror":"https://ror.org/02726j593","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210114158","https://openalex.org/I4210164537"]},{"id":"https://openalex.org/I4210127387","display_name":"Siberian Branch of the Russian Academy of Sciences","ror":"https://ror.org/02frkq021","country_code":"RU","type":"government","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210127387"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Svetlana Solodusha","raw_affiliation_strings":["Melentiev Energy Systems Institute, Siberian Branch of the Russian Academy of Sciences, 664033 Irkutsk, Russia"],"raw_orcid":"https://orcid.org/0000-0001-6162-7542","affiliations":[{"raw_affiliation_string":"Melentiev Energy Systems Institute, Siberian Branch of the Russian Academy of Sciences, 664033 Irkutsk, Russia","institution_ids":["https://openalex.org/I4210114158","https://openalex.org/I4210127387"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5090692957"],"corresponding_institution_ids":["https://openalex.org/I4210114158","https://openalex.org/I4210127387"],"apc_list":{"value":2100,"currency":"CHF","value_usd":2336},"apc_paid":{"value":2100,"currency":"CHF","value_usd":2336},"fwci":0.3489,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.46752042,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":95},"biblio":{"volume":"11","issue":"13","first_page":"2881","last_page":"2881"},"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":0.9955999851226807,"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":0.9955999851226807,"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":0.003800000064074993,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","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/boundary-control","display_name":"boundary control","score":0.9559999704360962},{"id":"https://openalex.org/keywords/heat-equation","display_name":"heat equation","score":0.7940000295639038},{"id":"https://openalex.org/keywords/heat-exchange-with-environment","display_name":"heat exchange with environment","score":0.6579999923706055},{"id":"https://openalex.org/keywords/controllability","display_name":"controllability","score":0.7020000219345093},{"id":"https://openalex.org/keywords/separation-of-variables","display_name":"separation of variables","score":0.7730000019073486},{"id":"https://openalex.org/keywords/constructive-control","display_name":"constructive control","score":0.4490000009536743}],"concepts":[{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.639869213104248},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.6308615207672119},{"id":"https://openalex.org/C204530211","wikidata":"https://www.wikidata.org/wiki/Q752823","display_name":"Thermal","level":2,"score":0.6095425486564636},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.5821684002876282},{"id":"https://openalex.org/C536315585","wikidata":"https://www.wikidata.org/wiki/Q7698332","display_name":"Temperature control","level":2,"score":0.5756509304046631},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.5240448117256165},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.521987795829773},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.492047518491745},{"id":"https://openalex.org/C188414643","wikidata":"https://www.wikidata.org/wiki/Q3001183","display_name":"Harmonics","level":3,"score":0.4898764491081238},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.45562151074409485},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4156275987625122},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.3968718945980072},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3586847186088562},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2883414626121521},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2662430703639984},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24928122758865356},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.23675191402435303},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.22297364473342896},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19442516565322876},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.16620489954948425},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.07902505993843079},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/math11132881","doi":"https://doi.org/10.3390/math11132881","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math11132881","pdf_url":"https://www.mdpi.com/2227-7390/11/13/2881/pdf?version=1687860875","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:gam:jmathe:v:11:y:2023:i:13:p:2881-:d:1180601","doi":null,"is_oa":false,"landing_page_url":"https://www.mdpi.com/2227-7390/11/13/2881/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:eb26895599394cd08e049bcbb02227ea","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/eb26895599394cd08e049bcbb02227ea","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics, Vol 11, Iss 13, p 2881 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/math11132881","doi":"https://doi.org/10.3390/math11132881","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math11132881","pdf_url":"https://www.mdpi.com/2227-7390/11/13/2881/pdf?version=1687860875","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3134435030","display_name":null,"funder_award_id":"FWEU-2021-0006","funder_id":"https://openalex.org/F4320327494","funder_display_name":"Ministry of Science and Higher Education of the Russian Federation"},{"id":"https://openalex.org/G448734546","display_name":null,"funder_award_id":"13.CKP.21.0038","funder_id":"https://openalex.org/F4320327494","funder_display_name":"Ministry of Science and Higher Education of the Russian Federation"}],"funders":[{"id":"https://openalex.org/F4320327494","display_name":"Ministry of Science and Higher Education of the Russian Federation","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4382402166.pdf","grobid_xml":"https://content.openalex.org/works/W4382402166.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W776962657","https://openalex.org/W2004014771","https://openalex.org/W2034276086","https://openalex.org/W2043909370","https://openalex.org/W2062786255","https://openalex.org/W2071010538","https://openalex.org/W2157713021","https://openalex.org/W2765579318","https://openalex.org/W2782536469","https://openalex.org/W4384934324"],"related_works":["https://openalex.org/W4384934324","https://openalex.org/W1818183303","https://openalex.org/W1988237270","https://openalex.org/W1986943420","https://openalex.org/W2566572848","https://openalex.org/W2136367978","https://openalex.org/W4283821169","https://openalex.org/W7164744721","https://openalex.org/W2903917540","https://openalex.org/W1797358562"],"abstract_inverted_index":{"This":[0],"paper":[1],"considers":[2],"a":[3,73,101,106,110],"rod":[4,32,48,90,99,133,171],"with":[5,19],"an":[6,153],"insulated":[7],"side":[8],"surface,":[9],"at":[10,85,166],"the":[11,20,27,31,36,39,43,47,54,64,78,82,86,89,93,98,117,123,128,132,139,156,162,167,170,173],"edges":[12],"of":[13,38,56,58,66,68,81,88,127,131,155,169],"which":[14],"there":[15],"is":[16,24,33],"heat":[17],"exchange":[18],"external":[21],"environment.":[22],"It":[23],"assumed":[25],"that":[26,91,122],"thermal":[28,44],"process":[29],"in":[30,46,97,136],"controlled":[34],"by":[35],"effect":[37],"ambient":[40],"temperature":[41,83,94,129,163],"on":[42,63],"state":[45,95,104,108],"through":[49],"its":[50],"boundary":[51,124],"temperatures.":[52],"Using":[53],"technique":[55],"separation":[57],"variables":[59],"and":[60,119,149],"methods":[61],"based":[62],"theory":[65],"control":[67,79,125,164],"finite-dimensional":[69],"systems,":[70],"we":[71,159],"propose":[72],"constructive":[74],"approach":[75],"to":[76,105,141],"build":[77],"function":[80],"conditions":[84],"ends":[87,168],"change":[92],"distribution":[96],"from":[100],"given":[102],"initial":[103,148],"final":[107,150],"within":[109],"specified":[111],"time":[112],"interval.":[113],"We":[114],"have":[115,160],"formulated":[116],"necessary":[118],"sufficient":[120],"condition":[121],"functions":[126,165],"modes":[130],"must":[134],"satisfy":[135],"order":[137],"for":[138,172],"problem":[140],"be":[142],"completely":[143],"controllable":[144],"under":[145],"any":[146],"allowable":[147],"conditions.":[151],"As":[152],"application":[154],"proposed":[157],"approach,":[158],"built":[161],"first":[174],"two":[175],"harmonics.":[176]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2023-06-29T00:00:00"}
