{"id":"https://openalex.org/W2285523682","doi":"https://doi.org/10.3233/asy-151339","title":"Mathematical justification of the obstacle problem in the case of piezoelectric plate","display_name":"Mathematical justification of the obstacle problem in the case of piezoelectric plate","publication_year":2016,"publication_date":"2016-02-12","ids":{"openalex":"https://openalex.org/W2285523682","doi":"https://doi.org/10.3233/asy-151339","mag":"2285523682"},"language":"en","primary_location":{"id":"doi:10.3233/asy-151339","is_oa":false,"landing_page_url":"https://doi.org/10.3233/asy-151339","pdf_url":null,"source":{"id":"https://openalex.org/S141283892","display_name":"Asymptotic Analysis","issn_l":"0921-7134","issn":["0921-7134","1875-8576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asymptotic 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/A5101431450","display_name":"Yan Guan","orcid":null},"institutions":[{"id":"https://openalex.org/I21945476","display_name":"Shanghai Normal University","ror":"https://ror.org/01cxqmw89","country_code":"CN","type":"education","lineage":["https://openalex.org/I21945476"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Guan Yan","raw_affiliation_strings":["Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China. E-mails:\u00a0gypyly@aliyun.com,\u00a0bernadette.miara@gmail.com"],"affiliations":[{"raw_affiliation_string":"Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China. E-mails:\u00a0gypyly@aliyun.com,\u00a0bernadette.miara@gmail.com","institution_ids":["https://openalex.org/I21945476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062798078","display_name":"Bernadette Miara","orcid":null},"institutions":[{"id":"https://openalex.org/I21945476","display_name":"Shanghai Normal University","ror":"https://ror.org/01cxqmw89","country_code":"CN","type":"education","lineage":["https://openalex.org/I21945476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bernadette Miara","raw_affiliation_strings":["Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China. E-mails:\u00a0gypyly@aliyun.com,\u00a0bernadette.miara@gmail.com"],"affiliations":[{"raw_affiliation_string":"Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China. E-mails:\u00a0gypyly@aliyun.com,\u00a0bernadette.miara@gmail.com","institution_ids":["https://openalex.org/I21945476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101431450"],"corresponding_institution_ids":["https://openalex.org/I21945476"],"apc_list":null,"apc_paid":null,"fwci":1.7174,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.81639017,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"96","issue":"3-4","first_page":"283","last_page":"308"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11799","display_name":"Adhesion, Friction, and Surface Interactions","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11799","display_name":"Adhesion, Friction, and Surface Interactions","score":0.9997000098228455,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9990000128746033,"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":0.9980000257492065,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/piezoelectricity","display_name":"Piezoelectricity","score":0.815606951713562},{"id":"https://openalex.org/keywords/displacement","display_name":"Displacement (psychology)","score":0.6006940007209778},{"id":"https://openalex.org/keywords/obstacle","display_name":"Obstacle","score":0.5939881205558777},{"id":"https://openalex.org/keywords/electric-field","display_name":"Electric field","score":0.5866153240203857},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5440523028373718},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4942212402820587},{"id":"https://openalex.org/keywords/electric-potential","display_name":"Electric potential","score":0.4873140752315521},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.47022557258605957},{"id":"https://openalex.org/keywords/electric-displacement-field","display_name":"Electric displacement field","score":0.45708394050598145},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4240213632583618},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4199531674385071},{"id":"https://openalex.org/keywords/transverse-plane","display_name":"Transverse plane","score":0.41523364186286926},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.38511064648628235},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.382618248462677},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.358795702457428},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2697597146034241},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.1773081123828888},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.16585507988929749},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.10610637068748474},{"id":"https://openalex.org/keywords/voltage","display_name":"Voltage","score":0.07169774174690247}],"concepts":[{"id":"https://openalex.org/C100082104","wikidata":"https://www.wikidata.org/wiki/Q183759","display_name":"Piezoelectricity","level":2,"score":0.815606951713562},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.6006940007209778},{"id":"https://openalex.org/C2776650193","wikidata":"https://www.wikidata.org/wiki/Q264661","display_name":"Obstacle","level":2,"score":0.5939881205558777},{"id":"https://openalex.org/C60799052","wikidata":"https://www.wikidata.org/wiki/Q46221","display_name":"Electric field","level":2,"score":0.5866153240203857},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5440523028373718},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4942212402820587},{"id":"https://openalex.org/C58570533","wikidata":"https://www.wikidata.org/wiki/Q55451","display_name":"Electric potential","level":3,"score":0.4873140752315521},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.47022557258605957},{"id":"https://openalex.org/C57470404","wikidata":"https://www.wikidata.org/wiki/Q371907","display_name":"Electric displacement field","level":3,"score":0.45708394050598145},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4240213632583618},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4199531674385071},{"id":"https://openalex.org/C154954056","wikidata":"https://www.wikidata.org/wiki/Q1604164","display_name":"Transverse plane","level":2,"score":0.41523364186286926},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.38511064648628235},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.382618248462677},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.358795702457428},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2697597146034241},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.1773081123828888},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.16585507988929749},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.10610637068748474},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.07169774174690247},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/asy-151339","is_oa":false,"landing_page_url":"https://doi.org/10.3233/asy-151339","pdf_url":null,"source":{"id":"https://openalex.org/S141283892","display_name":"Asymptotic Analysis","issn_l":"0921-7134","issn":["0921-7134","1875-8576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asymptotic Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322374","display_name":"Shanghai Normal University","ror":"https://ror.org/01cxqmw89"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W18535182","https://openalex.org/W1196376971","https://openalex.org/W1522494372","https://openalex.org/W1969777600","https://openalex.org/W1977466033","https://openalex.org/W1993608133","https://openalex.org/W2531370240","https://openalex.org/W2596000764","https://openalex.org/W2798512682","https://openalex.org/W3091814460"],"related_works":["https://openalex.org/W2374769878","https://openalex.org/W2045491918","https://openalex.org/W2914998743","https://openalex.org/W612753350","https://openalex.org/W2031123327","https://openalex.org/W1968932604","https://openalex.org/W4220671703","https://openalex.org/W2053328841","https://openalex.org/W2082933792","https://openalex.org/W2347775377"],"abstract_inverted_index":{"This":[0],"paper":[1],"aims":[2],"at":[3,70],"properly":[4],"justifying":[5],"the":[6,28,35,38,47,50,55,59,62,71,73,78,91,99,112,125],"modeling":[7],"of":[8,49,54,61,98,116],"a":[9,17,85,104],"thin":[10,123],"piezoelectric":[11,88,126],"plate":[12,63],"in":[13],"unilateral":[14],"contact":[15],"with":[16],"rigid":[18],"plane.":[19],"In":[20],"order":[21],"to":[22,65],"do":[23],"that":[24],"we":[25,45],"start":[26],"from":[27],"three-dimensional":[29],"non-linear":[30],"Signorini":[31],"problem":[32],"which":[33],"couples":[34],"elastic":[36,75,106],"and":[37,53,77,83,102,119],"electric":[39,56,79,100],"effects.":[40],"By":[41],"an":[42],"asymptotic":[43],"analysis":[44],"study":[46],"convergence":[48],"displacement":[51,94],"field":[52],"potential":[57,80],"as":[58],"thickness":[60],"goes":[64],"zero.":[66],"We":[67,109],"establish":[68],"that,":[69,121],"limit,":[72],"in-plane":[74],"components":[76],"are":[81],"coupled":[82],"solve":[84],"bilateral":[86],"linear":[87],"problem.":[89,108],"However":[90],"transverse":[92],"mechanical":[93],"field,":[95],"is":[96],"independent":[97],"effect":[101,128],"solves":[103],"two-dimensional":[105],"obstacle":[107],"also":[110],"investigate":[111],"very":[113],"popular":[114],"case":[115],"cubic":[117],"crystals":[118],"show":[120],"for":[122],"plates,":[124],"coupling":[127],"disappears.":[129]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}