{"id":"https://openalex.org/W2025475434","doi":"https://doi.org/10.1109/cdc.2011.6160382","title":"An algebraic solution method for the unsteady Hamilton-Jacobi equation","display_name":"An algebraic solution method for the unsteady Hamilton-Jacobi equation","publication_year":2011,"publication_date":"2011-12-01","ids":{"openalex":"https://openalex.org/W2025475434","doi":"https://doi.org/10.1109/cdc.2011.6160382","mag":"2025475434"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2011.6160382","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6160382","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","raw_type":"proceedings-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/A5035690333","display_name":"Yu Kawano","orcid":"https://orcid.org/0000-0001-5066-4700"},"institutions":[{"id":"https://openalex.org/I98285908","display_name":"Osaka University","ror":"https://ror.org/035t8zc32","country_code":"JP","type":"education","lineage":["https://openalex.org/I98285908"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Yu Kawano","raw_affiliation_strings":["Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, Japan","Graduate School of Engineering Science, Osaka University, Toyonaka, 560-8531, Japan"],"affiliations":[{"raw_affiliation_string":"Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, Japan","institution_ids":["https://openalex.org/I98285908"]},{"raw_affiliation_string":"Graduate School of Engineering Science, Osaka University, Toyonaka, 560-8531, Japan","institution_ids":["https://openalex.org/I98285908"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014103535","display_name":"Toshiyuki Ohtsuka","orcid":"https://orcid.org/0000-0003-3554-8933"},"institutions":[{"id":"https://openalex.org/I98285908","display_name":"Osaka University","ror":"https://ror.org/035t8zc32","country_code":"JP","type":"education","lineage":["https://openalex.org/I98285908"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Toshiyuki Ohtsuka","raw_affiliation_strings":["Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, Japan","Graduate School of Engineering Science, Osaka University, Toyonaka, 560-8531, Japan"],"affiliations":[{"raw_affiliation_string":"Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, Japan","institution_ids":["https://openalex.org/I98285908"]},{"raw_affiliation_string":"Graduate School of Engineering Science, Osaka University, Toyonaka, 560-8531, Japan","institution_ids":["https://openalex.org/I98285908"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5035690333"],"corresponding_institution_ids":["https://openalex.org/I98285908"],"apc_list":null,"apc_paid":null,"fwci":0.3773,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.57107044,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"7741","last_page":"7746"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9968000054359436,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9915000200271606,"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/meromorphic-function","display_name":"Meromorphic function","score":0.8105067014694214},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7025589346885681},{"id":"https://openalex.org/keywords/function-field-of-an-algebraic-variety","display_name":"Function field of an algebraic variety","score":0.5797533988952637},{"id":"https://openalex.org/keywords/algebraic-function","display_name":"Algebraic function","score":0.5716946721076965},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5691956281661987},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.5660691261291504},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5326648950576782},{"id":"https://openalex.org/keywords/algebraic-solution","display_name":"Algebraic solution","score":0.5243397355079651},{"id":"https://openalex.org/keywords/dimension-of-an-algebraic-variety","display_name":"Dimension of an algebraic variety","score":0.502863347530365},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.5019762516021729},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4706769585609436},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi-equation","display_name":"Hamilton\u2013Jacobi equation","score":0.46619999408721924},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.44236382842063904},{"id":"https://openalex.org/keywords/real-algebraic-geometry","display_name":"Real algebraic geometry","score":0.44065284729003906},{"id":"https://openalex.org/keywords/algebraic-extension","display_name":"Algebraic extension","score":0.41317999362945557},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4112905263900757},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3682938814163208},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3392001688480377},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27787503600120544},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.19065308570861816},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.14869701862335205},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.13413095474243164}],"concepts":[{"id":"https://openalex.org/C190333341","wikidata":"https://www.wikidata.org/wiki/Q217616","display_name":"Meromorphic function","level":2,"score":0.8105067014694214},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7025589346885681},{"id":"https://openalex.org/C10996884","wikidata":"https://www.wikidata.org/wiki/Q5508773","display_name":"Function field of an algebraic variety","level":3,"score":0.5797533988952637},{"id":"https://openalex.org/C148607811","wikidata":"https://www.wikidata.org/wiki/Q746863","display_name":"Algebraic function","level":3,"score":0.5716946721076965},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5691956281661987},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.5660691261291504},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5326648950576782},{"id":"https://openalex.org/C87563608","wikidata":"https://www.wikidata.org/wiki/Q2900186","display_name":"Algebraic solution","level":5,"score":0.5243397355079651},{"id":"https://openalex.org/C25971838","wikidata":"https://www.wikidata.org/wiki/Q5277261","display_name":"Dimension of an algebraic variety","level":3,"score":0.502863347530365},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.5019762516021729},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4706769585609436},{"id":"https://openalex.org/C2778860007","wikidata":"https://www.wikidata.org/wiki/Q1060137","display_name":"Hamilton\u2013Jacobi equation","level":2,"score":0.46619999408721924},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.44236382842063904},{"id":"https://openalex.org/C2731732","wikidata":"https://www.wikidata.org/wiki/Q7301119","display_name":"Real algebraic geometry","level":3,"score":0.44065284729003906},{"id":"https://openalex.org/C89290136","wikidata":"https://www.wikidata.org/wiki/Q550791","display_name":"Algebraic extension","level":5,"score":0.41317999362945557},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4112905263900757},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3682938814163208},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3392001688480377},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27787503600120544},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.19065308570861816},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.14869701862335205},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.13413095474243164},{"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2011.6160382","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6160382","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W645921674","https://openalex.org/W1487586009","https://openalex.org/W1516061036","https://openalex.org/W1522531528","https://openalex.org/W1605757990","https://openalex.org/W1931868030","https://openalex.org/W1971122553","https://openalex.org/W1978363680","https://openalex.org/W2049707341","https://openalex.org/W2093834886","https://openalex.org/W2109640889","https://openalex.org/W2113350382","https://openalex.org/W2126479355","https://openalex.org/W2142322632","https://openalex.org/W2155948924","https://openalex.org/W2321396669","https://openalex.org/W2595399821","https://openalex.org/W2736427745","https://openalex.org/W2992532933","https://openalex.org/W3134175739","https://openalex.org/W3186624155","https://openalex.org/W4212872652","https://openalex.org/W4298054792"],"related_works":["https://openalex.org/W2170846659","https://openalex.org/W4256397181","https://openalex.org/W4233049353","https://openalex.org/W2019519844","https://openalex.org/W4387637555","https://openalex.org/W2320751405","https://openalex.org/W1502419693","https://openalex.org/W2408624816","https://openalex.org/W2039329794","https://openalex.org/W1996217084"],"abstract_inverted_index":{"The":[0],"unsteady":[1,31],"Hamilton-Jacobi":[2],"equation":[3],"(HJE)":[4],"plays":[5],"an":[6,74,81,107,111],"important":[7],"role":[8],"in":[9,60,88],"the":[10,30,48,93,99,103],"analysis":[11],"and":[12,17,44,52,78,83,98],"control":[13],"of":[14,42,47,62,96,102,122],"nonlinear":[15,25],"systems":[16],"is":[18,50,66,109],"very":[19],"difficult":[20],"to":[21,39],"solve":[22],"for":[23,33],"general":[24],"systems.":[26],"In":[27],"this":[28],"paper,":[29],"HJE":[32],"a":[34,71,89,120],"Hamiltonian":[35],"with":[36,55,73],"coefficients":[37],"belonging":[38],"meromorphic":[40,94],"functions":[41,46,95,101],"time":[43,97],"rational":[45,100],"state":[49],"considered,":[51],"its":[53],"solutions":[54],"algebraic":[56,75,112,123],"gradients":[57],"are":[58],"characterized":[59],"terms":[61],"commutative":[63],"algebra.":[64],"It":[65],"shown":[67],"that":[68],"there":[69],"exists":[70,87],"solution":[72],"gradient":[76,113],"if":[77,80],"only":[79,118],"H-invariant":[82],"involutive":[84],"maximal":[85],"ideal":[86,108],"polynomial":[90],"ring":[91],"over":[92],"state.":[104],"If":[105],"such":[106],"found,":[110],"can":[114],"be":[115],"obtained":[116],"by":[117],"solving":[119],"set":[121],"equations.":[124]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
