{"id":"https://openalex.org/W3138678299","doi":"https://doi.org/10.1007/s40314-021-01488-5","title":"Some numerical results for control of 3D heat equations using Nash equilibrium","display_name":"Some numerical results for control of 3D heat equations using Nash equilibrium","publication_year":2021,"publication_date":"2021-03-22","ids":{"openalex":"https://openalex.org/W3138678299","doi":"https://doi.org/10.1007/s40314-021-01488-5","mag":"3138678299"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-021-01488-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-021-01488-5","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"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":"Computational and Applied Mathematics","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/A5048158651","display_name":"Pit\u00e1goras Pinheiro de Carvalho","orcid":"https://orcid.org/0000-0003-0949-2921"},"institutions":[{"id":"https://openalex.org/I3123346794","display_name":"Universidade Estadual do Piau\u00ed","ror":"https://ror.org/02na6tz09","country_code":"BR","type":"education","lineage":["https://openalex.org/I3123346794"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Pit\u00e1goras Pinheiro de Carvalho","raw_affiliation_strings":["Coordena\u00e7\u00e3o de Matem\u00e1tica - Universidade Estadual do Piau\u00ed, Teresina, PI, Brazil"],"raw_orcid":"https://orcid.org/0000-0003-0949-2921","affiliations":[{"raw_affiliation_string":"Coordena\u00e7\u00e3o de Matem\u00e1tica - Universidade Estadual do Piau\u00ed, Teresina, PI, Brazil","institution_ids":["https://openalex.org/I3123346794"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5048158651"],"corresponding_institution_ids":["https://openalex.org/I3123346794"],"apc_list":null,"apc_paid":null,"fwci":0.2775,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.52235188,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"40","issue":"3","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":0.996999979019165,"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":0.996999979019165,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9941999912261963,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9908000230789185,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6929872035980225},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.6832118630409241},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5698339343070984},{"id":"https://openalex.org/keywords/matlab","display_name":"MATLAB","score":0.5341882705688477},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5152474045753479},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.49573028087615967},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44674667716026306},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4448584318161011},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4349084496498108},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.43318912386894226},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4329758286476135},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4308550953865051},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1873653531074524},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08087629079818726}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6929872035980225},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.6832118630409241},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5698339343070984},{"id":"https://openalex.org/C2780365114","wikidata":"https://www.wikidata.org/wiki/Q169478","display_name":"MATLAB","level":2,"score":0.5341882705688477},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5152474045753479},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.49573028087615967},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44674667716026306},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4448584318161011},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4349084496498108},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.43318912386894226},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4329758286476135},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4308550953865051},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1873653531074524},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08087629079818726},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40314-021-01488-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-021-01488-5","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"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":"Computational and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1579672749","https://openalex.org/W1594213283","https://openalex.org/W1967993296","https://openalex.org/W2001902033","https://openalex.org/W2062278141","https://openalex.org/W2082187902","https://openalex.org/W2094479990","https://openalex.org/W2321928279","https://openalex.org/W2330024298","https://openalex.org/W2491284009","https://openalex.org/W2499815172","https://openalex.org/W2613994990","https://openalex.org/W2796539113","https://openalex.org/W2802290342","https://openalex.org/W2808019040","https://openalex.org/W2899333491","https://openalex.org/W2941416714","https://openalex.org/W2970754047","https://openalex.org/W3002484093","https://openalex.org/W3082038209","https://openalex.org/W3084152656","https://openalex.org/W4234761190"],"related_works":["https://openalex.org/W2387966793","https://openalex.org/W1975833764","https://openalex.org/W2088468004","https://openalex.org/W2012186120","https://openalex.org/W2119544289","https://openalex.org/W2538854589","https://openalex.org/W1979076981","https://openalex.org/W3082038209","https://openalex.org/W4283332940","https://openalex.org/W3174503691"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}