{"id":"https://openalex.org/W2010523745","doi":"https://doi.org/10.1007/s10915-009-9303-3","title":"Computer Assisted Proofs of Bifurcating Solutions for\u00a0Nonlinear Heat Convection Problems","display_name":"Computer Assisted Proofs of Bifurcating Solutions for\u00a0Nonlinear Heat Convection Problems","publication_year":2009,"publication_date":"2009-06-29","ids":{"openalex":"https://openalex.org/W2010523745","doi":"https://doi.org/10.1007/s10915-009-9303-3","mag":"2010523745"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-009-9303-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-009-9303-3","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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":"Journal of Scientific Computing","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/A5066956728","display_name":"Mitsuhiro Nakao","orcid":"https://orcid.org/0000-0002-0980-0114"},"institutions":[{"id":"https://openalex.org/I135598925","display_name":"Kyushu University","ror":"https://ror.org/00p4k0j84","country_code":"JP","type":"education","lineage":["https://openalex.org/I135598925"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Mitsuhiro T. Nakao","raw_affiliation_strings":["Faculty of Mathematics, Kyushu University, 6-10-1 Higashi-Ku Hakozaki, Fukuoka, 812-8581, Japan","Kyushu University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Kyushu University, 6-10-1 Higashi-Ku Hakozaki, Fukuoka, 812-8581, Japan","institution_ids":["https://openalex.org/I135598925"]},{"raw_affiliation_string":"Kyushu University","institution_ids":["https://openalex.org/I135598925"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020726356","display_name":"Yoshitaka Watanabe","orcid":"https://orcid.org/0000-0001-6520-3552"},"institutions":[{"id":"https://openalex.org/I135598925","display_name":"Kyushu University","ror":"https://ror.org/00p4k0j84","country_code":"JP","type":"education","lineage":["https://openalex.org/I135598925"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yoshitaka Watanabe","raw_affiliation_strings":["Research Institute for Information Technology, Kyushu University, Fukuoka, Japan","Kyushu University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research Institute for Information Technology, Kyushu University, Fukuoka, Japan","institution_ids":["https://openalex.org/I135598925"]},{"raw_affiliation_string":"Kyushu University","institution_ids":["https://openalex.org/I135598925"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112254994","display_name":"Nobito Yamamoto","orcid":null},"institutions":[{"id":"https://openalex.org/I20529979","display_name":"University of Electro-Communications","ror":"https://ror.org/02x73b849","country_code":"JP","type":"education","lineage":["https://openalex.org/I20529979"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Nobito Yamamoto","raw_affiliation_strings":["Department of Computer Science and Information Mathematics, The University of Electro-Communications, Tokyo, Japan","the University of Electro-Communications"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Information Mathematics, The University of Electro-Communications, Tokyo, Japan","institution_ids":["https://openalex.org/I20529979"]},{"raw_affiliation_string":"the University of Electro-Communications","institution_ids":["https://openalex.org/I20529979"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037784397","display_name":"Takaaki Nishida","orcid":"https://orcid.org/0000-0003-3042-0180"},"institutions":[{"id":"https://openalex.org/I150744194","display_name":"Waseda University","ror":"https://ror.org/00ntfnx83","country_code":"JP","type":"education","lineage":["https://openalex.org/I150744194"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Takaaki Nishida","raw_affiliation_strings":["Faculty of Science and Engineering, Waseda University, Tokyo, Japan","Waseda University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Science and Engineering, Waseda University, Tokyo, Japan","institution_ids":["https://openalex.org/I150744194"]},{"raw_affiliation_string":"Waseda University","institution_ids":["https://openalex.org/I150744194"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052599648","display_name":"Myoung-Nyoung Kim","orcid":null},"institutions":[{"id":"https://openalex.org/I135598925","display_name":"Kyushu University","ror":"https://ror.org/00p4k0j84","country_code":"JP","type":"education","lineage":["https://openalex.org/I135598925"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Myoung-Nyoung Kim","raw_affiliation_strings":["Faculty of Mathematics, Kyushu University, 6-10-1 Higashi-Ku Hakozaki, Fukuoka, 812-8581, Japan","Kyushu University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Kyushu University, 6-10-1 Higashi-Ku Hakozaki, Fukuoka, 812-8581, Japan","institution_ids":["https://openalex.org/I135598925"]},{"raw_affiliation_string":"Kyushu University","institution_ids":["https://openalex.org/I135598925"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5066956728"],"corresponding_institution_ids":["https://openalex.org/I135598925"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.7701,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.76020328,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"43","issue":"3","first_page":"388","last_page":"401"},"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":0.9905999898910522,"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":0.9905999898910522,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9789999723434448,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9750999808311462,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8072786331176758},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7602218389511108},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6794794797897339},{"id":"https://openalex.org/keywords/convection","display_name":"Convection","score":0.5726513862609863},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5229447484016418},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45951879024505615},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4544042944908142},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4456072747707367},{"id":"https://openalex.org/keywords/rayleigh-number","display_name":"Rayleigh number","score":0.429240345954895},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4196210205554962},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38032373785972595},{"id":"https://openalex.org/keywords/natural-convection","display_name":"Natural convection","score":0.25172531604766846},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16504263877868652},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.13166147470474243},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1282234787940979},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07126682996749878}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8072786331176758},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7602218389511108},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6794794797897339},{"id":"https://openalex.org/C10899652","wikidata":"https://www.wikidata.org/wiki/Q160329","display_name":"Convection","level":2,"score":0.5726513862609863},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5229447484016418},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45951879024505615},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4544042944908142},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4456072747707367},{"id":"https://openalex.org/C106836276","wikidata":"https://www.wikidata.org/wiki/Q898249","display_name":"Rayleigh number","level":4,"score":0.429240345954895},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4196210205554962},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38032373785972595},{"id":"https://openalex.org/C54791560","wikidata":"https://www.wikidata.org/wiki/Q3285020","display_name":"Natural convection","level":3,"score":0.25172531604766846},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16504263877868652},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.13166147470474243},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1282234787940979},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07126682996749878},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10915-009-9303-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-009-9303-3","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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":"Journal of Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.41999998688697815}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W87867753","https://openalex.org/W1975021587","https://openalex.org/W1991606206","https://openalex.org/W1996282011","https://openalex.org/W1998595723","https://openalex.org/W2017981826","https://openalex.org/W2023794945","https://openalex.org/W2029194063","https://openalex.org/W2055931342","https://openalex.org/W2066629027","https://openalex.org/W2080037133","https://openalex.org/W2092068986","https://openalex.org/W2468331248","https://openalex.org/W2991415348","https://openalex.org/W4236855339","https://openalex.org/W4249273983","https://openalex.org/W6644102186"],"related_works":["https://openalex.org/W2808944898","https://openalex.org/W3196207352","https://openalex.org/W4283721563","https://openalex.org/W4386810572","https://openalex.org/W1968681582","https://openalex.org/W2606608893","https://openalex.org/W755150155","https://openalex.org/W2022268999","https://openalex.org/W2055179441","https://openalex.org/W2040890853"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-19T17:40:00.097472","created_date":"2025-10-10T00:00:00"}
