{"id":"https://openalex.org/W2028836744","doi":"https://doi.org/10.1137/110832343","title":"Large Time Behavior of Solutions of Hamilton--Jacobi--Bellman Equations with Quadratic Nonlinearity in Gradients","display_name":"Large Time Behavior of Solutions of Hamilton--Jacobi--Bellman Equations with Quadratic Nonlinearity in Gradients","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2028836744","doi":"https://doi.org/10.1137/110832343","mag":"2028836744"},"language":"en","primary_location":{"id":"doi:10.1137/110832343","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110832343","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","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/A5024797861","display_name":"Naoyuki Ichihara","orcid":"https://orcid.org/0000-0002-9744-3240"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Naoyuki Ichihara","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5007752209","display_name":"Shuenn\u2010Jyi Sheu","orcid":"https://orcid.org/0000-0001-9605-5599"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shuenn-Jyi Sheu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024797861"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":10.378,"has_fulltext":false,"cited_by_count":42,"citation_normalized_percentile":{"value":0.98173748,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"45","issue":"1","first_page":"279","last_page":"306"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9925000071525574,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9882000088691711,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8757479786872864},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.6482163071632385},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6409633755683899},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi-equation","display_name":"Hamilton\u2013Jacobi equation","score":0.6074603199958801},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.6058174967765808},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5715615749359131},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.5458231568336487},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5426142811775208},{"id":"https://openalex.org/keywords/cauchy-problem","display_name":"Cauchy problem","score":0.5105920433998108},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43309149146080017},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.43188905715942383},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.42659473419189453}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8757479786872864},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.6482163071632385},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6409633755683899},{"id":"https://openalex.org/C2778860007","wikidata":"https://www.wikidata.org/wiki/Q1060137","display_name":"Hamilton\u2013Jacobi equation","level":2,"score":0.6074603199958801},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.6058174967765808},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5715615749359131},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.5458231568336487},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5426142811775208},{"id":"https://openalex.org/C153635880","wikidata":"https://www.wikidata.org/wiki/Q1412436","display_name":"Cauchy problem","level":3,"score":0.5105920433998108},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43309149146080017},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.43188905715942383},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.42659473419189453},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/110832343","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110832343","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:EPrintsHUMATH:2091","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922805","display_name":"EPrints - Department of Mathematics, Hokkaido University","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":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"A minisemester on evolution of interfaces, Sapporo 2010","raw_type":"Conference or Workshop Item"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1494380031","https://openalex.org/W1982142979","https://openalex.org/W1992759804","https://openalex.org/W1996270146","https://openalex.org/W1998598781","https://openalex.org/W2003588897","https://openalex.org/W2013338783","https://openalex.org/W2022729976","https://openalex.org/W2044948548","https://openalex.org/W2053068479","https://openalex.org/W2055173039","https://openalex.org/W2067390362","https://openalex.org/W2076319278","https://openalex.org/W2085806849","https://openalex.org/W2093303153","https://openalex.org/W2178442254","https://openalex.org/W3037124231","https://openalex.org/W3104160683"],"related_works":["https://openalex.org/W3207047935","https://openalex.org/W1601266269","https://openalex.org/W2036444760","https://openalex.org/W3195796642","https://openalex.org/W2400581667","https://openalex.org/W4213342640","https://openalex.org/W2049761058","https://openalex.org/W2345019225","https://openalex.org/W2078366360","https://openalex.org/W1993693184"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,9,39,42,50],"large":[3],"time":[4,35],"behavior":[5],"of":[6,22,41,49],"solutions":[7],"to":[8,37,46],"Cauchy":[10,43],"problem":[11,44],"for":[12],"semilinear":[13],"parabolic":[14],"equations":[15],"having":[16],"quadratic":[17],"nonlinearity":[18],"in":[19,26],"gradients.":[20],"Equations":[21],"this":[23],"kind":[24],"appear":[25],"stochastic":[27],"control":[28],"theory.":[29],"It":[30],"turns":[31],"out":[32],"that":[33],"as":[34],"tends":[36],"infinity":[38],"solution":[40,48],"converges":[45],"a":[47],"associated":[51],"ergodic":[52],"problem.":[53],"Our":[54],"approach":[55],"relies":[56],"on":[57],"PDE":[58],"and":[59],"probabilistic":[60],"arguments.":[61]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}