{"id":"https://openalex.org/W2031779751","doi":"https://doi.org/10.1137/s0036139996292015","title":"Spectrum and Stability for Elastic Systems with Global or Local Kelvin--Voigt Damping","display_name":"Spectrum and Stability for Elastic Systems with Global or Local Kelvin--Voigt Damping","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W2031779751","doi":"https://doi.org/10.1137/s0036139996292015","mag":"2031779751"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139996292015","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139996292015","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/A5019371433","display_name":"Kangsheng Liu","orcid":"https://orcid.org/0000-0001-8985-7294"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Kangsheng Liu","raw_affiliation_strings":["Zhejiang, University"],"affiliations":[{"raw_affiliation_string":"Zhejiang, University","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100668202","display_name":"Shuping Chen","orcid":"https://orcid.org/0000-0002-2388-7156"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shuping Chen","raw_affiliation_strings":["Zhejiang, University"],"affiliations":[{"raw_affiliation_string":"Zhejiang, University","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024422562","display_name":"Zhuangyi Liu","orcid":"https://orcid.org/0000-0002-0540-5264"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhuangyi Liu","raw_affiliation_strings":["Zhejiang University"],"affiliations":[{"raw_affiliation_string":"Zhejiang University","institution_ids":["https://openalex.org/I76130692"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5019371433"],"corresponding_institution_ids":["https://openalex.org/I76130692"],"apc_list":null,"apc_paid":null,"fwci":0.8331,"has_fulltext":false,"cited_by_count":145,"citation_normalized_percentile":{"value":0.72256626,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"59","issue":"2","first_page":"651","last_page":"668"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":1.0,"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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9915000200271606,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.9034872055053711},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.7036282420158386},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6166871786117554},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5294997692108154},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.5059656500816345},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.46895354986190796},{"id":"https://openalex.org/keywords/string","display_name":"String (physics)","score":0.4623047411441803},{"id":"https://openalex.org/keywords/thermoelastic-damping","display_name":"Thermoelastic damping","score":0.4470255374908447},{"id":"https://openalex.org/keywords/exponential-decay","display_name":"Exponential decay","score":0.444824755191803},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4235846996307373},{"id":"https://openalex.org/keywords/vibration","display_name":"Vibration","score":0.41289377212524414},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.24666890501976013},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1357080340385437}],"concepts":[{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.9034872055053711},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.7036282420158386},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6166871786117554},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5294997692108154},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.5059656500816345},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.46895354986190796},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.4623047411441803},{"id":"https://openalex.org/C92458943","wikidata":"https://www.wikidata.org/wiki/Q7783171","display_name":"Thermoelastic damping","level":3,"score":0.4470255374908447},{"id":"https://openalex.org/C180188523","wikidata":"https://www.wikidata.org/wiki/Q574576","display_name":"Exponential decay","level":2,"score":0.444824755191803},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4235846996307373},{"id":"https://openalex.org/C198394728","wikidata":"https://www.wikidata.org/wiki/Q3695508","display_name":"Vibration","level":2,"score":0.41289377212524414},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.24666890501976013},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1357080340385437},{"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/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C204530211","wikidata":"https://www.wikidata.org/wiki/Q752823","display_name":"Thermal","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036139996292015","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139996292015","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":25,"referenced_works":["https://openalex.org/W320153183","https://openalex.org/W599293027","https://openalex.org/W1495844786","https://openalex.org/W1519619947","https://openalex.org/W1526200187","https://openalex.org/W1527296550","https://openalex.org/W1532154335","https://openalex.org/W1555942143","https://openalex.org/W1575147392","https://openalex.org/W1590111042","https://openalex.org/W1974599443","https://openalex.org/W2005722356","https://openalex.org/W2019955665","https://openalex.org/W2021627713","https://openalex.org/W2036202965","https://openalex.org/W2053168208","https://openalex.org/W2071007460","https://openalex.org/W2075110727","https://openalex.org/W2081721226","https://openalex.org/W2088313014","https://openalex.org/W2314636969","https://openalex.org/W2491079642","https://openalex.org/W2795084044","https://openalex.org/W4236945040","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2515867266","https://openalex.org/W4293575531","https://openalex.org/W4321787545","https://openalex.org/W2924465594","https://openalex.org/W3106150653","https://openalex.org/W4298181152","https://openalex.org/W4386136165","https://openalex.org/W2560261823","https://openalex.org/W2964850913","https://openalex.org/W1557658044"],"abstract_inverted_index":{"In":[0,35],"this":[1],"paper,":[2],"we":[3],"study":[4],"the":[5,17,22,28,40,43,51,53,56,63,66,73,83,94,112],"mathematical":[6],"properties":[7],"of":[8,21,50,55,62,65,85,111],"a":[9,86,101],"variational":[10],"second":[11],"order":[12],"evolution":[13],"equation,":[14],"which":[15,103],"includes":[16],"equations":[18],"modelling":[19],"vibrations":[20],"Euler--Bernoulli":[23],"and":[24,47],"Rayleigh":[25],"beams":[26],"with":[27,108],"global":[29],"or":[30],"local":[31],"Kelvin--Voigt":[32],"(K--V)":[33],"damping.":[34,74],"particular,":[36],"our":[37],"results":[38],"describe":[39],"semigroup":[41,67],"setting,":[42],"strong":[44],"asymptotic":[45],"stability":[46,49],"exponential":[48],"semigroup,":[52,57],"analyticity":[54],"as":[58,60],"well":[59],"characteristics":[61],"spectrum":[64],"generator":[68],"under":[69],"various":[70],"conditions":[71],"on":[72,100],"We":[75],"also":[76],"give":[77],"an":[78],"example":[79],"to":[80],"show":[81],"that":[82],"energy":[84],"vibrating":[87],"string":[88],"does":[89],"not":[90],"decay":[91],"exponentially":[92],"when":[93],"K--V":[95],"damping":[96],"is":[97],"distributed":[98],"only":[99],"subinterval":[102],"has":[104],"one":[105,109],"end":[106,110],"coincident":[107],"string.":[113]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":15},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}