{"id":"https://openalex.org/W592304891","doi":"https://doi.org/10.1137/140979447","title":"The Transition to a Point Constraint in a Mixed Biharmonic Eigenvalue Problem","display_name":"The Transition to a Point Constraint in a Mixed Biharmonic Eigenvalue Problem","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W592304891","doi":"https://doi.org/10.1137/140979447","mag":"592304891"},"language":"en","primary_location":{"id":"doi:10.1137/140979447","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140979447","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","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/A5072176272","display_name":"Alan E. Lindsay","orcid":"https://orcid.org/0000-0001-8221-8668"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. E. Lindsay","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037517718","display_name":"Michael J. Ward","orcid":"https://orcid.org/0000-0001-6959-7202"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. J. Ward","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5015774352","display_name":"Th\u00e9odore Kolokolnikov","orcid":"https://orcid.org/0000-0002-7179-4325"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"T. Kolokolnikov","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4537,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.81896389,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"75","issue":"3","first_page":"1193","last_page":"1224"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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/T11558","display_name":"Composite Material Mechanics","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6201492547988892},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5753608345985413},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5570557117462158},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5455044507980347},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.5410264134407043},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5379742980003357},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5088198781013489},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5007495880126953},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.48030322790145874},{"id":"https://openalex.org/keywords/biharmonic-equation","display_name":"Biharmonic equation","score":0.4572261869907379},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4320177733898163},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4237844944000244},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.4118589162826538},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3840569853782654},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.31247326731681824},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.17432910203933716}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6201492547988892},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5753608345985413},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5570557117462158},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5455044507980347},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.5410264134407043},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5379742980003357},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5088198781013489},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5007495880126953},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.48030322790145874},{"id":"https://openalex.org/C145784156","wikidata":"https://www.wikidata.org/wiki/Q859808","display_name":"Biharmonic equation","level":3,"score":0.4572261869907379},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4320177733898163},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4237844944000244},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.4118589162826538},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3840569853782654},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.31247326731681824},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.17432910203933716},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/140979447","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140979447","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W84888134","https://openalex.org/W1501601053","https://openalex.org/W1574775234","https://openalex.org/W1677236203","https://openalex.org/W2012172263","https://openalex.org/W2013004758","https://openalex.org/W2022915277","https://openalex.org/W2024732454","https://openalex.org/W2037622031","https://openalex.org/W2046023215","https://openalex.org/W2047294225","https://openalex.org/W2047898167","https://openalex.org/W2119873577","https://openalex.org/W2120062331","https://openalex.org/W2129180949","https://openalex.org/W2133940857","https://openalex.org/W2137308669","https://openalex.org/W2170539123","https://openalex.org/W3102819843","https://openalex.org/W3170586200"],"related_works":["https://openalex.org/W2503543076","https://openalex.org/W2738351852","https://openalex.org/W1131942522","https://openalex.org/W3139424580","https://openalex.org/W1986396960","https://openalex.org/W2105227268","https://openalex.org/W4307213029","https://openalex.org/W1989880152","https://openalex.org/W1977275827","https://openalex.org/W58429384"],"abstract_inverted_index":{"The":[0,221],"mixed-order":[1,132],"eigenvalue":[2,133,195],"problem":[3,75,134],"$-\\delta":[4,108],"\\Delta^2":[5,109],"u":[6,9,12],"+":[7,10],"\\Delta":[8],"\\lambda":[11],"=":[13],"0$":[14,142],"with":[15,96,112],"$\\delta>0$,":[16],"modeling":[17],"small":[18,37,62,98,105],"amplitude":[19],"vibrations":[20],"of":[21,39,54,60,90,127,130,148,155,172,179,182,199,216,233],"a":[22,28,35,94,97,208],"thin":[23],"plate,":[24],"is":[25,196,203],"analyzed":[26],"in":[27,93,137,187],"bounded":[29],"two-dimensional":[30],"domain":[31,95],"$\\Omega$":[32,55],"that":[33,206],"contains":[34],"single":[36],"hole":[38,99,122,184],"radius":[40,181],"$\\varepsilon$":[41],"centered":[42],"at":[43],"some":[44],"$x_0\\in":[45],"\\Omega$.":[46],"Clamped":[47],"conditions":[48],"are":[49,100,135,150,227],"imposed":[50],"on":[51,57,117,120],"the":[52,58,61,65,73,80,88,91,104,121,124,128,131,138,169,175,180,183,188,194,211,217,225,234],"boundary":[53,59,115],"and":[56,69,119,143,163],"hole.":[63],"In":[64,168],"limit":[66,140],"$\\varepsilon\\to":[67,141],"0$,":[68],"for":[70,76,152,224],"$\\delta={\\mathcal":[71,161,219],"O}(1)$,":[72],"limiting":[74,176],"$u$":[77],"must":[78],"satisfy":[79],"additional":[81,114],"point":[82,212],"constraint":[83,213],"$u(x_0)=0$.":[84],"To":[85],"determine":[86],"how":[87],"eigenvalues":[89,129,149,226],"Laplacian":[92],"perturbed":[101],"by":[102,229],"adding":[103],"fourth-order":[106],"term":[107],"u$,":[110],"together":[111],"an":[113],"condition":[116],"$\\partial\\Omega$":[118],"boundary,":[123],"asymptotic":[125,222],"behavior":[126,177,214],"studied":[136],"dual":[139],"$\\delta\\to":[144],"0$.":[145],"Leading-order":[146],"behaviors":[147],"determined":[151],"three":[153],"ranges":[154],"$\\delta\\ll":[156,158],"1$:":[157],"{\\mathcal":[159],"O}(\\varepsilon^2)$,":[160,162],"${\\mathcal":[164,190],"O}(\\varepsilon^2)\\ll":[165,191],"\\delta\\ll":[166,192],"1$.":[167],"first":[170],"two":[171],"these":[173],"regimes,":[174],"depends":[178],"$\\varepsilon$,":[185],"while":[186],"regime":[189,205],"1$":[193],"asymptotically":[197],"independent":[198],"$\\varepsilon$.":[200],"Therefore,":[201],"it":[202],"this":[204],"provides":[207],"transition":[209],"to":[210],"characteristic":[215],"range":[218],"O}(1)$.":[220],"results":[223],"validated":[228],"full":[230],"numerical":[231],"simulations":[232],"PDE.":[235]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}