{"id":"https://openalex.org/W2018699077","doi":"https://doi.org/10.1137/s003614100343055x","title":"An Elliptic Problem Related to Planar Vortex Pairs","display_name":"An Elliptic Problem Related to Planar Vortex Pairs","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2018699077","doi":"https://doi.org/10.1137/s003614100343055x","mag":"2018699077"},"language":"en","primary_location":{"id":"doi:10.1137/s003614100343055x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s003614100343055x","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/A5002493025","display_name":"Gongbao Li","orcid":"https://orcid.org/0000-0002-2389-5391"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gongbao Li","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049252278","display_name":"Shusen Yan","orcid":"https://orcid.org/0000-0002-3559-0042"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shusen Yan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100297667","display_name":"Jianfu Yang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jianfu Yang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5002493025"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":34,"citation_normalized_percentile":{"value":0.12931522,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"36","issue":"5","first_page":"1444","last_page":"1460"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9986000061035156,"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"}},"topics":[{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9986000061035156,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9894000291824341,"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/lambda","display_name":"Lambda","score":0.8021203875541687},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.7527594566345215},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.668613851070404},{"id":"https://openalex.org/keywords/harmonic-function","display_name":"Harmonic function","score":0.5820607542991638},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5683963894844055},{"id":"https://openalex.org/keywords/vortex","display_name":"Vortex","score":0.49907779693603516},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.49805617332458496},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4960528314113617},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4891336262226105},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3327668011188507},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2946018576622009},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.123379647731781}],"concepts":[{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.8021203875541687},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.7527594566345215},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.668613851070404},{"id":"https://openalex.org/C627467","wikidata":"https://www.wikidata.org/wiki/Q599027","display_name":"Harmonic function","level":2,"score":0.5820607542991638},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5683963894844055},{"id":"https://openalex.org/C140820882","wikidata":"https://www.wikidata.org/wiki/Q732722","display_name":"Vortex","level":2,"score":0.49907779693603516},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.49805617332458496},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4960528314113617},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4891336262226105},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3327668011188507},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2946018576622009},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.123379647731781},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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":2,"locations":[{"id":"doi:10.1137/s003614100343055x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s003614100343055x","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:rune.une.edu.au:1959.11/4284","is_oa":false,"landing_page_url":"https://hdl.handle.net/1959.11/4284","pdf_url":null,"source":{"id":"https://openalex.org/S7407055448","display_name":"RUNE (Research UNE)","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.siam.org/journals/sima.php","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":11,"referenced_works":["https://openalex.org/W1981288703","https://openalex.org/W1982357817","https://openalex.org/W1997513007","https://openalex.org/W2004044311","https://openalex.org/W2053065715","https://openalex.org/W2061543546","https://openalex.org/W2071068303","https://openalex.org/W2074026523","https://openalex.org/W2085058754","https://openalex.org/W2118283004","https://openalex.org/W2135247737"],"related_works":["https://openalex.org/W4387497383","https://openalex.org/W3183948672","https://openalex.org/W3173606202","https://openalex.org/W3110381201","https://openalex.org/W2948807893","https://openalex.org/W2778153218","https://openalex.org/W2758277628","https://openalex.org/W1531601525","https://openalex.org/W3089826093","https://openalex.org/W4287650493"],"abstract_inverted_index":{"In":[0],"this":[1,90],"paper,":[2],"we":[3,64],"study":[4],"the":[5,11,16,41,46,58,77],"existence":[6],"and":[7],"limiting":[8],"behavior":[9],"of":[10,15,45,55,74],"mountain":[12],"pass":[13],"solutions":[14],"elliptic":[17],"problem":[18],"$-\\Delta":[19],"u":[20],"=":[21],"\\lambda":[22],"f(u-q(x))$":[23],"in":[24],"$\\Omega\\subset":[25],"R^2;":[26],"u=":[27],"0$":[28],"on":[29,57,76],"$\\partial\\Omega$,":[30,79],"where":[31],"q":[32,56],"is":[33],"a":[34,51,82],"positive":[35],"harmonic":[36],"function.":[37],"We":[38],"show":[39,65],"that":[40,66],"\"vortex":[42],"core\"":[43],"$A_\\lambda=\\{x\\in\\Omega:u_\\lambda(x)>q(x)\\}$":[44],"solution":[47,83],"$u_\\lambda$":[48,84],"shrinks":[49,88],"to":[50,89],"global":[52],"minimum":[53,71,93],"point":[54,73,94],"boundary":[59,78],"$\\partial\\Omega$":[60],"as":[61,96],"$\\lambda\\to+\\infty$.":[62,97],"Furthermore,":[63],"for":[67],"each":[68],"strict":[69,91],"local":[70,92],"$x_0$":[72,95],"$q(x)$":[75],"there":[80],"exists":[81],"whose":[85],"vortex":[86],"core":[87]},"counts_by_year":[{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}