{"id":"https://openalex.org/W1966535662","doi":"https://doi.org/10.1137/120862545","title":"Uniform Decay Rates for the Wave Equation with Nonlinear Damping Locally Distributed in Unbounded Domains with Finite Measure","display_name":"Uniform Decay Rates for the Wave Equation with Nonlinear Damping Locally Distributed in Unbounded Domains with Finite Measure","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W1966535662","doi":"https://doi.org/10.1137/120862545","mag":"1966535662"},"language":"en","primary_location":{"id":"doi:10.1137/120862545","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120862545","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","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/A5088209758","display_name":"Marcelo M. Cavalcanti","orcid":"https://orcid.org/0000-0001-5493-5918"},"institutions":[{"id":"https://openalex.org/I123443094","display_name":"Universidade Estadual de Maring\u00e1","ror":"https://ror.org/04bqqa360","country_code":"BR","type":"education","lineage":["https://openalex.org/I123443094"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Marcelo M. Cavalcanti","raw_affiliation_strings":["State University of Maring\u00e1"],"affiliations":[{"raw_affiliation_string":"State University of Maring\u00e1","institution_ids":["https://openalex.org/I123443094"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071721084","display_name":"Fl\u00e1vio R. Dias Silva","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fl\u00e1vio R. Dias Silva","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5049035398","display_name":"V. N. Domingos Cavalcanti","orcid":"https://orcid.org/0000-0002-1047-3763"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Val\u00e9ria N. Domingos Cavalcanti","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5088209758"],"corresponding_institution_ids":["https://openalex.org/I123443094"],"apc_list":null,"apc_paid":null,"fwci":2.4346,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.89084836,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"52","issue":"1","first_page":"545","last_page":"580"},"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":0.9998999834060669,"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":0.9998999834060669,"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":0.9980000257492065,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9940999746322632,"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/omega","display_name":"Omega","score":0.8554747104644775},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.699001669883728},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5979188084602356},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5750481486320496},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.5665937662124634},{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.550446629524231},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.46942952275276184},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46317392587661743},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.4467596411705017},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.4456423819065094},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.43487727642059326},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3261936902999878},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1371060609817505}],"concepts":[{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.8554747104644775},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.699001669883728},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5979188084602356},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5750481486320496},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.5665937662124634},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.550446629524231},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.46942952275276184},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46317392587661743},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.4467596411705017},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.4456423819065094},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.43487727642059326},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3261936902999878},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1371060609817505},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/120862545","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120862545","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.5299999713897705,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W588153840","https://openalex.org/W1489222793","https://openalex.org/W1513902134","https://openalex.org/W1545761024","https://openalex.org/W1586623601","https://openalex.org/W1597700183","https://openalex.org/W1664623743","https://openalex.org/W1866311589","https://openalex.org/W1966382600","https://openalex.org/W1970001989","https://openalex.org/W1973549460","https://openalex.org/W1979907077","https://openalex.org/W1991099802","https://openalex.org/W1992906838","https://openalex.org/W1992941868","https://openalex.org/W2007032224","https://openalex.org/W2011232312","https://openalex.org/W2012886830","https://openalex.org/W2014171178","https://openalex.org/W2023542822","https://openalex.org/W2026523808","https://openalex.org/W2030901661","https://openalex.org/W2038683990","https://openalex.org/W2042567026","https://openalex.org/W2049094266","https://openalex.org/W2051026540","https://openalex.org/W2057804709","https://openalex.org/W2061079050","https://openalex.org/W2074718504","https://openalex.org/W2087574051","https://openalex.org/W2088779465","https://openalex.org/W2103846364","https://openalex.org/W2127464980","https://openalex.org/W2128004971","https://openalex.org/W2169525530","https://openalex.org/W2172250835","https://openalex.org/W2227150130","https://openalex.org/W2249223893","https://openalex.org/W2257184362","https://openalex.org/W2526639416","https://openalex.org/W2963944298","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2371200319","https://openalex.org/W2367609594","https://openalex.org/W2350320737","https://openalex.org/W238609530","https://openalex.org/W2391455523","https://openalex.org/W2739518152","https://openalex.org/W2053400769","https://openalex.org/W2020692468","https://openalex.org/W4376122670","https://openalex.org/W4388093492"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,46,72,102],"concerned":[3],"with":[4,16,20,51],"the":[5,8,13,17,65,69,108],"study":[6],"of":[7,12,68,107,110],"uniform":[9],"decay":[10],"rates":[11],"energy":[14],"associated":[15],"wave":[18],"equation":[19],"nonlinear":[21],"damping":[22],"locally":[23],"distributed":[24],"$u_{tt}":[25],"-\\Delta":[26],"u":[27],"+a(x)\\,g(u_t)":[28],"=0":[29],"~\\hbox{":[30],"in":[31,81,88,105],"}\\Omega":[32],"\\times":[33],"(0,\\infty)$":[34],"subject":[35],"to":[36,74],"Dirichlet":[37],"boundary":[38,57],"conditions":[39],"where":[40,91,114],"$\\Omega":[41],"\\subset":[42],"\\mathbb{R}^n$":[43],"$n\\geq":[44],"2$":[45],"an":[47],"unbounded":[48,55],"open":[49],"set":[50],"finite":[52],"measure":[53],"and":[54,77,100],"smooth":[56],"$\\partial":[58],"\\Omega=\\Gamma$.":[59],"The":[60],"function":[61],"$a(x)$,":[62],"responsible":[63],"for":[64],"localized":[66],"effect":[67],"dissipative":[70],"mechanism,":[71],"assumed":[73],"be":[75],"nonnegative":[76],"essentially":[78],"bounded":[79],"and,":[80],"addition,":[82],"$a(x)":[83],"\\geq":[84],"a_0":[85],">0~\\hbox{":[86],"a.e.\\":[87],"}":[89],"~\\omega,$":[90],"$\\omega=\\omega'":[92],"\\cup":[93],"\\{x":[94],"\\in":[95,116],"\\Omega;||x||":[96,117],">":[97],"R\\}$":[98],"($R>0$)":[99],"$\\omega'$":[101],"a":[103],"neighborhood":[104],"$\\Omega$":[106],"closure":[109],"$\\partial\\Omega":[111],"\\cap":[112],"B_R$,":[113],"$B_R=\\{x":[115],"<":[118],"R\\}$.":[119]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}