{"id":"https://openalex.org/W2041310730","doi":"https://doi.org/10.1137/09077117x","title":"Dynamical Solutions of Singular Wave Equations Modeling Electrostatic MEMS","display_name":"Dynamical Solutions of Singular Wave Equations Modeling Electrostatic MEMS","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2041310730","doi":"https://doi.org/10.1137/09077117x","mag":"2041310730"},"language":"en","primary_location":{"id":"doi:10.1137/09077117x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/09077117x","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Dynamical Systems","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/A5113521787","display_name":"Yujin Guo","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yujin Guo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5113521787"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.7359,"has_fulltext":false,"cited_by_count":44,"citation_normalized_percentile":{"value":0.94966239,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"9","issue":"4","first_page":"1135","last_page":"1163"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9988999962806702,"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":0.9988999962806702,"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/T11565","display_name":"Thermoelastic and Magnetoelastic Phenomena","score":0.9983999729156494,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/lambda","display_name":"Lambda","score":0.7918848991394043},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5522477626800537},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5045884847640991},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4813409745693207},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.47118380665779114},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4556460976600647},{"id":"https://openalex.org/keywords/elastic-instability","display_name":"Elastic instability","score":0.44564545154571533},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31532037258148193},{"id":"https://openalex.org/keywords/instability","display_name":"Instability","score":0.2680371403694153},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.19048291444778442}],"concepts":[{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.7918848991394043},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5522477626800537},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5045884847640991},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4813409745693207},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.47118380665779114},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4556460976600647},{"id":"https://openalex.org/C2776901185","wikidata":"https://www.wikidata.org/wiki/Q3799193","display_name":"Elastic instability","level":3,"score":0.44564545154571533},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31532037258148193},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.2680371403694153},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.19048291444778442}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/09077117x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/09077117x","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Dynamical Systems","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":21,"referenced_works":["https://openalex.org/W157591785","https://openalex.org/W1597209545","https://openalex.org/W1597700183","https://openalex.org/W1608211965","https://openalex.org/W1982314892","https://openalex.org/W2002436197","https://openalex.org/W2015309127","https://openalex.org/W2023590249","https://openalex.org/W2024105000","https://openalex.org/W2026906076","https://openalex.org/W2030511585","https://openalex.org/W2049857668","https://openalex.org/W2050359135","https://openalex.org/W2061391122","https://openalex.org/W2074334982","https://openalex.org/W2075034671","https://openalex.org/W2082458348","https://openalex.org/W2145306245","https://openalex.org/W2616933858","https://openalex.org/W2963794118","https://openalex.org/W3091814460"],"related_works":["https://openalex.org/W2951695430","https://openalex.org/W4300891849","https://openalex.org/W2318687609","https://openalex.org/W91590591","https://openalex.org/W159772521","https://openalex.org/W2950100995","https://openalex.org/W3170064006","https://openalex.org/W2281582664","https://openalex.org/W2554039769","https://openalex.org/W1997904316"],"abstract_inverted_index":{"We":[0],"study":[1],"a":[2,8,14,22,31,41,62,84,93,128],"fourth-order":[3],"singular":[4,9],"wave":[5],"equation":[6,20],"involving":[7],"nonlinear":[10],"term":[11],"${\\frac{\\lambda}{(1-u)^2}}$":[12],"in":[13],"bounded":[15],"domain":[16],"of":[17,30,57,102],"${\\mathbb{R}^N}$.":[18],"This":[19],"models":[21],"simple":[23],"electrostatic":[24],"microelectromechanical":[25],"system":[26],"(MEMS)":[27],"device":[28],"consisting":[29],"thin":[32],"elastic":[33,59,69,120,136],"plate":[34,44,70,121,137],"with":[35],"boundary":[36],"supported":[37],"at":[38,46,139],"0":[39],"above":[40],"rigid":[42],"ground":[43,74],"located":[45],"1.":[47],"Here":[48],"u":[49],"is":[50],"modeled":[51],"to":[52,127],"describe":[53],"the":[54,58,68,73,100,119,135],"dynamical":[55],"deflection":[56],"plate.":[60],"When":[61],"voltage\u2014represented":[63],"here":[64],"by":[65],"$\\lambda$\u2014is":[66],"applied,":[67],"deflects":[71],"towards":[72],"plate,":[75],"and":[76,124],"snap-through":[77],"(quenching)":[78],"may":[79],"occur":[80],"when":[81],"it":[82],"exceeds":[83],"certain":[85],"critical":[86],"value":[87],"$\\lambda^*$":[88],"(the":[89],"pull-in":[90,95],"voltage),":[91],"creating":[92],"so-called":[94],"instability,":[96],"which":[97],"greatly":[98],"affects":[99],"design":[101],"many":[103],"devices.":[104],"For":[105],"$1\\leq":[106],"N\\leq3$,":[107],"analytic":[108],"results":[109],"show":[110],"that":[111,116],"there":[112],"exist":[113],"$0<\\lambda_1\\leq\\lambda^*<\\infty$":[114],"such":[115],"for":[117,133],"$0\\leq\\lambda<\\lambda_1$":[118],"globally":[122],"exists":[123],"exponentially":[125],"converges":[126],"regular":[129],"steady":[130],"state,":[131],"while":[132],"$\\lambda>\\lambda^*$":[134],"quenches":[138],"finite":[140],"time.":[141]},"counts_by_year":[{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":11},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
