{"id":"https://openalex.org/W3015030207","doi":"https://doi.org/10.3390/sym12040517","title":"On the Cauchy Problem of Vectorial Thermostatted Kinetic Frameworks","display_name":"On the Cauchy Problem of Vectorial Thermostatted Kinetic Frameworks","publication_year":2020,"publication_date":"2020-04-02","ids":{"openalex":"https://openalex.org/W3015030207","doi":"https://doi.org/10.3390/sym12040517","mag":"3015030207"},"language":"en","primary_location":{"id":"doi:10.3390/sym12040517","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12040517","pdf_url":"https://www.mdpi.com/2073-8994/12/4/517/pdf?version=1587133099","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/12/4/517/pdf?version=1587133099","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067031673","display_name":"Carlo Bianca","orcid":"https://orcid.org/0000-0003-1122-7510"},"institutions":[{"id":"https://openalex.org/I2802505300","display_name":"\u00c9cole Sup\u00e9rieure d'Ing\u00e9nieurs en G\u00e9nie \u00c9lectrique","ror":"https://ror.org/01apwkd48","country_code":"FR","type":"education","lineage":["https://openalex.org/I2802505300"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Carlo Bianca","raw_affiliation_strings":["Laboratoire Quartz EA 7393, \u00c9cole Sup\u00e9rieure d\u2019Ing\u00e9nieurs en G\u00e9nie \u00c9lectrique, Productique et Management Industriel, 95092 Cergy Pontoise CEDEX, France","Laboratoire de Recherche en Eco-Innovation Industrielle et Energ\u00e9tique, \u00c9cole Sup\u00e9rieure d\u2019Ing\u00e9nieurs en G\u00e9nie \u00c9lectrique, Productique et Management Industriel, 95092 Cergy Pontoise CEDEX, France"],"raw_orcid":"https://orcid.org/0000-0003-1122-7510","affiliations":[{"raw_affiliation_string":"Laboratoire Quartz EA 7393, \u00c9cole Sup\u00e9rieure d\u2019Ing\u00e9nieurs en G\u00e9nie \u00c9lectrique, Productique et Management Industriel, 95092 Cergy Pontoise CEDEX, France","institution_ids":["https://openalex.org/I2802505300"]},{"raw_affiliation_string":"Laboratoire de Recherche en Eco-Innovation Industrielle et Energ\u00e9tique, \u00c9cole Sup\u00e9rieure d\u2019Ing\u00e9nieurs en G\u00e9nie \u00c9lectrique, Productique et Management Industriel, 95092 Cergy Pontoise CEDEX, France","institution_ids":["https://openalex.org/I2802505300"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085854765","display_name":"Bruno Carbonaro","orcid":"https://orcid.org/0000-0001-7102-6011"},"institutions":[{"id":"https://openalex.org/I197809005","display_name":"University of Campania \"Luigi Vanvitelli\"","ror":"https://ror.org/02kqnpp86","country_code":"IT","type":"education","lineage":["https://openalex.org/I197809005"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Bruno Carbonaro","raw_affiliation_strings":["Dipartimento di Matematica e Fisica, Universit\u00e0 degli Studi della Campania \u201cL. Vanvitelli\u201d, Viale Lincoln 5, I-81100 Caserta, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Fisica, Universit\u00e0 degli Studi della Campania \u201cL. Vanvitelli\u201d, Viale Lincoln 5, I-81100 Caserta, Italy","institution_ids":["https://openalex.org/I197809005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043488166","display_name":"Marco Menale","orcid":"https://orcid.org/0000-0001-8822-3038"},"institutions":[{"id":"https://openalex.org/I197809005","display_name":"University of Campania \"Luigi Vanvitelli\"","ror":"https://ror.org/02kqnpp86","country_code":"IT","type":"education","lineage":["https://openalex.org/I197809005"]},{"id":"https://openalex.org/I2802505300","display_name":"\u00c9cole Sup\u00e9rieure d'Ing\u00e9nieurs en G\u00e9nie \u00c9lectrique","ror":"https://ror.org/01apwkd48","country_code":"FR","type":"education","lineage":["https://openalex.org/I2802505300"]}],"countries":["FR","IT"],"is_corresponding":false,"raw_author_name":"Marco Menale","raw_affiliation_strings":["Dipartimento di Matematica e Fisica, Universit\u00e0 degli Studi della Campania \u201cL. Vanvitelli\u201d, Viale Lincoln 5, I-81100 Caserta, Italy","Laboratoire Quartz EA 7393, \u00c9cole Sup\u00e9rieure d\u2019Ing\u00e9nieurs en G\u00e9nie \u00c9lectrique, Productique et Management Industriel, 95092 Cergy Pontoise CEDEX, France"],"raw_orcid":"https://orcid.org/0000-0001-8822-3038","affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Fisica, Universit\u00e0 degli Studi della Campania \u201cL. Vanvitelli\u201d, Viale Lincoln 5, I-81100 Caserta, Italy","institution_ids":["https://openalex.org/I197809005"]},{"raw_affiliation_string":"Laboratoire Quartz EA 7393, \u00c9cole Sup\u00e9rieure d\u2019Ing\u00e9nieurs en G\u00e9nie \u00c9lectrique, Productique et Management Industriel, 95092 Cergy Pontoise CEDEX, France","institution_ids":["https://openalex.org/I2802505300"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5067031673"],"corresponding_institution_ids":["https://openalex.org/I2802505300"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.335,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.79602701,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"12","issue":"4","first_page":"517","last_page":"517"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9966999888420105,"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"}},"topics":[{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9966999888420105,"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"}},{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9901000261306763,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7522552013397217},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.6546916961669922},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.6026285290718079},{"id":"https://openalex.org/keywords/state-variable","display_name":"State variable","score":0.6022863984107971},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5735706090927124},{"id":"https://openalex.org/keywords/cauchy-problem","display_name":"Cauchy problem","score":0.5009398460388184},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4753251373767853},{"id":"https://openalex.org/keywords/non-equilibrium-thermodynamics","display_name":"Non-equilibrium thermodynamics","score":0.47491416335105896},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4445732533931732},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4387039542198181},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.41992366313934326},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3977698087692261},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3249353766441345},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24107354879379272},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23002570867538452},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.07521983981132507}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7522552013397217},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.6546916961669922},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.6026285290718079},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.6022863984107971},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5735706090927124},{"id":"https://openalex.org/C153635880","wikidata":"https://www.wikidata.org/wiki/Q1412436","display_name":"Cauchy problem","level":3,"score":0.5009398460388184},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4753251373767853},{"id":"https://openalex.org/C74859849","wikidata":"https://www.wikidata.org/wiki/Q2466686","display_name":"Non-equilibrium thermodynamics","level":2,"score":0.47491416335105896},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4445732533931732},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4387039542198181},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.41992366313934326},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3977698087692261},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3249353766441345},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24107354879379272},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23002570867538452},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.07521983981132507},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym12040517","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12040517","pdf_url":"https://www.mdpi.com/2073-8994/12/4/517/pdf?version=1587133099","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:d9e4310d7f5e4528929edc4edb52844c","is_oa":true,"landing_page_url":"https://doaj.org/article/d9e4310d7f5e4528929edc4edb52844c","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,"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":"Symmetry, Vol 12, Iss 4, p 517 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/4/517/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym12040517","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym12040517","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12040517","pdf_url":"https://www.mdpi.com/2073-8994/12/4/517/pdf?version=1587133099","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.5199999809265137,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W47643447","https://openalex.org/W590413840","https://openalex.org/W1521738998","https://openalex.org/W1540810403","https://openalex.org/W1646534854","https://openalex.org/W1826679922","https://openalex.org/W1992987816","https://openalex.org/W2004712234","https://openalex.org/W2006338292","https://openalex.org/W2011122873","https://openalex.org/W2017974675","https://openalex.org/W2018987171","https://openalex.org/W2022348550","https://openalex.org/W2027437004","https://openalex.org/W2029107725","https://openalex.org/W2038582967","https://openalex.org/W2058105398","https://openalex.org/W2059261907","https://openalex.org/W2066764855","https://openalex.org/W2075109082","https://openalex.org/W2075903724","https://openalex.org/W2094107452","https://openalex.org/W2112164016","https://openalex.org/W2131479976","https://openalex.org/W2155216551","https://openalex.org/W2603889387","https://openalex.org/W2651967647","https://openalex.org/W2790429949","https://openalex.org/W2810456100","https://openalex.org/W3023193022","https://openalex.org/W3101792382","https://openalex.org/W4213373779","https://openalex.org/W4388364567","https://openalex.org/W6601929159","https://openalex.org/W6657192588"],"related_works":["https://openalex.org/W2078366360","https://openalex.org/W2400581667","https://openalex.org/W2049761058","https://openalex.org/W4213342640","https://openalex.org/W2394174381","https://openalex.org/W4394654496","https://openalex.org/W2020390959","https://openalex.org/W2892071505","https://openalex.org/W2345019225","https://openalex.org/W1968696210"],"abstract_inverted_index":{"This":[0],"paper":[1,54],"is":[2,55,72,102],"devoted":[3],"to":[4,38],"the":[5,17,39,45,48,53,61,64,91,94,121],"derivation":[6],"and":[7,42,74,111,114],"mathematical":[8,35],"analysis":[9,36],"of":[10,19,44,47,79,82],"new":[11],"thermostatted":[12,65,95],"kinetic":[13],"theory":[14],"frameworks":[15],"for":[16],"modeling":[18],"nonequilibrium":[20],"complex":[21],"systems":[22,110],"composed":[23],"by":[24],"particles":[25],"whose":[26],"microscopic":[27],"state":[28,32],"includes":[29],"a":[30,68,80,98],"vectorial":[31,70,100],"variable.":[33],"The":[34,76],"refers":[37],"global":[40],"existence":[41],"uniqueness":[43],"solution":[46],"related":[49],"Cauchy":[50],"problem.":[51],"Specifically,":[52],"divided":[56],"in":[57,120],"two":[58],"parts.":[59],"In":[60,90],"first":[62],"part":[63,93],"framework":[66,77,96],"with":[67,86,97],"continuous":[69],"variable":[71,101],"proposed":[73],"analyzed.":[75],"consists":[78],"system":[81],"partial":[83],"integro-differential":[84],"equations":[85],"quadratic":[87],"type":[88],"nonlinearities.":[89],"second":[92],"discrete":[99],"investigated.":[103],"Real":[104],"world":[105],"applications,":[106],"such":[107],"as":[108],"social":[109],"crowd":[112],"dynamics,":[113],"future":[115],"research":[116],"directions":[117],"are":[118],"outlined":[119],"paper.":[122]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}