{"id":"https://openalex.org/W2804119183","doi":"https://doi.org/10.1007/s00498-018-0213-5","title":"Boundary energy control of a system governed by the nonlinear Klein\u2013Gordon equation","display_name":"Boundary energy control of a system governed by the nonlinear Klein\u2013Gordon equation","publication_year":2018,"publication_date":"2018-03-01","ids":{"openalex":"https://openalex.org/W2804119183","doi":"https://doi.org/10.1007/s00498-018-0213-5","mag":"2804119183"},"language":"en","primary_location":{"id":"doi:10.1007/s00498-018-0213-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00498-018-0213-5","pdf_url":null,"source":{"id":"https://openalex.org/S88345224","display_name":"Mathematics of Control Signals and Systems","issn_l":"0932-4194","issn":["0932-4194","1435-568X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Control, Signals, and Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000808861","display_name":"\u041c. \u0412. \u0414\u043e\u043b\u0433\u043e\u043f\u043e\u043b\u0438\u043a","orcid":"https://orcid.org/0000-0003-0677-0797"},"institutions":[{"id":"https://openalex.org/I173089394","display_name":"ITMO University","ror":"https://ror.org/04txgxn49","country_code":"RU","type":"education","lineage":["https://openalex.org/I173089394"]},{"id":"https://openalex.org/I4210142628","display_name":"Institute of Problems of Mechanical Engineering","ror":"https://ror.org/047pt5178","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210142628","https://openalex.org/I4210164537"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Maksim Dolgopolik","raw_affiliation_strings":["ITMO University, Saint Petersburg, Russia","Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, Saint Petersburg, Russia"],"raw_orcid":"https://orcid.org/0000-0003-0677-0797","affiliations":[{"raw_affiliation_string":"ITMO University, Saint Petersburg, Russia","institution_ids":["https://openalex.org/I173089394"]},{"raw_affiliation_string":"Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, Saint Petersburg, Russia","institution_ids":["https://openalex.org/I4210142628"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047874759","display_name":"\u0410lexander L. Fradkov","orcid":"https://orcid.org/0000-0002-5633-0944"},"institutions":[{"id":"https://openalex.org/I172901346","display_name":"St Petersburg University","ror":"https://ror.org/023znxa73","country_code":"RU","type":"education","lineage":["https://openalex.org/I172901346"]},{"id":"https://openalex.org/I173089394","display_name":"ITMO University","ror":"https://ror.org/04txgxn49","country_code":"RU","type":"education","lineage":["https://openalex.org/I173089394"]},{"id":"https://openalex.org/I4210142628","display_name":"Institute of Problems of Mechanical Engineering","ror":"https://ror.org/047pt5178","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210142628","https://openalex.org/I4210164537"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Alexander L. Fradkov","raw_affiliation_strings":["ITMO University, Saint Petersburg, Russia","Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, Saint Petersburg, Russia","Saint Petersburg State University, Saint Petersburg, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ITMO University, Saint Petersburg, Russia","institution_ids":["https://openalex.org/I173089394"]},{"raw_affiliation_string":"Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, Saint Petersburg, Russia","institution_ids":["https://openalex.org/I4210142628"]},{"raw_affiliation_string":"Saint Petersburg State University, Saint Petersburg, Russia","institution_ids":["https://openalex.org/I172901346"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083175703","display_name":"Boris Andrievsky","orcid":"https://orcid.org/0000-0001-6323-2931"},"institutions":[{"id":"https://openalex.org/I172901346","display_name":"St Petersburg University","ror":"https://ror.org/023znxa73","country_code":"RU","type":"education","lineage":["https://openalex.org/I172901346"]},{"id":"https://openalex.org/I173089394","display_name":"ITMO University","ror":"https://ror.org/04txgxn49","country_code":"RU","type":"education","lineage":["https://openalex.org/I173089394"]},{"id":"https://openalex.org/I4210142628","display_name":"Institute of Problems of Mechanical Engineering","ror":"https://ror.org/047pt5178","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210142628","https://openalex.org/I4210164537"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Boris Andrievsky","raw_affiliation_strings":["ITMO University, Saint Petersburg, Russia","Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, Saint Petersburg, Russia","Saint Petersburg State University, Saint Petersburg, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ITMO University, Saint Petersburg, Russia","institution_ids":["https://openalex.org/I173089394"]},{"raw_affiliation_string":"Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, Saint Petersburg, Russia","institution_ids":["https://openalex.org/I4210142628"]},{"raw_affiliation_string":"Saint Petersburg State University, Saint Petersburg, Russia","institution_ids":["https://openalex.org/I172901346"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5000808861","https://openalex.org/A5047874759","https://openalex.org/A5083175703"],"corresponding_institution_ids":["https://openalex.org/I172901346","https://openalex.org/I173089394","https://openalex.org/I4210142628"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":1.1754,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.78043782,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"30","issue":"1","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":0.9998999834060669,"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":0.9998999834060669,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7553579807281494},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.6814585328102112},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.5938181281089783},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5851618051528931},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5792785882949829},{"id":"https://openalex.org/keywords/string","display_name":"String (physics)","score":0.5458701848983765},{"id":"https://openalex.org/keywords/klein\u2013gordon-equation","display_name":"Klein\u2013Gordon equation","score":0.5245956778526306},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.45882320404052734},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44322243332862854},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4405299127101898},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.3816061317920685},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36630457639694214},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.22567981481552124},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20135948061943054},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.12001439929008484}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7553579807281494},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6814585328102112},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.5938181281089783},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5851618051528931},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5792785882949829},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.5458701848983765},{"id":"https://openalex.org/C101682238","wikidata":"https://www.wikidata.org/wiki/Q868967","display_name":"Klein\u2013Gordon equation","level":3,"score":0.5245956778526306},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.45882320404052734},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44322243332862854},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4405299127101898},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3816061317920685},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36630457639694214},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.22567981481552124},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20135948061943054},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.12001439929008484},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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":1,"locations":[{"id":"doi:10.1007/s00498-018-0213-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00498-018-0213-5","pdf_url":null,"source":{"id":"https://openalex.org/S88345224","display_name":"Mathematics of Control Signals and Systems","issn_l":"0932-4194","issn":["0932-4194","1435-568X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Control, Signals, and Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.6700000166893005}],"awards":[{"id":"https://openalex.org/G244381746","display_name":null,"funder_award_id":"17-08-01728","funder_id":"https://openalex.org/F4320321079","funder_display_name":"Russian Foundation for Basic Research"},{"id":"https://openalex.org/G4718128360","display_name":null,"funder_award_id":"14\u201029\u201000142","funder_id":"https://openalex.org/F4320324099","funder_display_name":"Russian Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"},{"id":"https://openalex.org/F4320324099","display_name":"Russian Science Foundation","ror":"https://ror.org/03y2gwe85"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W299921089","https://openalex.org/W585688435","https://openalex.org/W633013857","https://openalex.org/W647474111","https://openalex.org/W792360124","https://openalex.org/W1072261708","https://openalex.org/W1097058110","https://openalex.org/W1598317411","https://openalex.org/W1966575940","https://openalex.org/W1972435886","https://openalex.org/W1982372749","https://openalex.org/W1993230642","https://openalex.org/W1993746420","https://openalex.org/W2012552707","https://openalex.org/W2013232999","https://openalex.org/W2028022198","https://openalex.org/W2028789196","https://openalex.org/W2031521898","https://openalex.org/W2032668029","https://openalex.org/W2041521369","https://openalex.org/W2047598119","https://openalex.org/W2050493032","https://openalex.org/W2058263458","https://openalex.org/W2062421509","https://openalex.org/W2071809716","https://openalex.org/W2075727229","https://openalex.org/W2076802130","https://openalex.org/W2077446806","https://openalex.org/W2093376917","https://openalex.org/W2093427566","https://openalex.org/W2104011177","https://openalex.org/W2136774549","https://openalex.org/W2144144709","https://openalex.org/W2150467770","https://openalex.org/W2185433014","https://openalex.org/W2496815638","https://openalex.org/W2545656754","https://openalex.org/W2553060111","https://openalex.org/W2558781461","https://openalex.org/W4298039342"],"related_works":["https://openalex.org/W2115030441","https://openalex.org/W2147578878","https://openalex.org/W2159990075","https://openalex.org/W2047785777","https://openalex.org/W1977673410","https://openalex.org/W2094931821","https://openalex.org/W1556508989","https://openalex.org/W4288944437","https://openalex.org/W4206452777","https://openalex.org/W2951215589"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":6}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}