{"id":"https://openalex.org/W2887233488","doi":"https://doi.org/10.1137/16m1100514","title":"Stability for the Mixed Problem Involving the Wave Equation, with Localized Damping, in Unbounded Domains with Finite Measure","display_name":"Stability for the Mixed Problem Involving the Wave Equation, with Localized Damping, in Unbounded Domains with Finite Measure","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2887233488","doi":"https://doi.org/10.1137/16m1100514","mag":"2887233488"},"language":"en","primary_location":{"id":"doi:10.1137/16m1100514","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1100514","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":[],"countries":[],"is_corresponding":true,"raw_author_name":"Marcelo M. Cavalcanti","raw_affiliation_strings":[],"affiliations":[]},{"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":"middle","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":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5000869705","display_name":"Andr\u00e9 Vicente","orcid":"https://orcid.org/0000-0001-6404-326X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andr\u00e9 Vicente","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5088209758"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1235,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.79154873,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"56","issue":"4","first_page":"2802","last_page":"2834"},"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":0.9988999962806702,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9936000108718872,"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/mathematics","display_name":"Mathematics","score":0.8561897277832031},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.683358371257782},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6043455600738525},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5654932260513306},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.5553111433982849},{"id":"https://openalex.org/keywords/open-set","display_name":"Open set","score":0.5439770221710205},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5264041423797607},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.5108978152275085},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4939163327217102},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.4639173746109009},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4391612112522125},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.41954877972602844},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33187806606292725},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.21385648846626282}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8561897277832031},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.683358371257782},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6043455600738525},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5654932260513306},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.5553111433982849},{"id":"https://openalex.org/C42357961","wikidata":"https://www.wikidata.org/wiki/Q213363","display_name":"Open set","level":2,"score":0.5439770221710205},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5264041423797607},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.5108978152275085},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4939163327217102},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.4639173746109009},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4391612112522125},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.41954877972602844},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33187806606292725},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.21385648846626282},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m1100514","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1100514","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":[{"score":0.8600000143051147,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G2641574347","display_name":null,"funder_award_id":"151/2014","funder_id":"https://openalex.org/F4320322772","funder_display_name":"Funda\u00e7\u00e3o Arauc\u00e1ria"},{"id":"https://openalex.org/G4805389198","display_name":null,"funder_award_id":"304895/2003-2","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G5658082774","display_name":null,"funder_award_id":"300631/2003-0","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"}],"funders":[{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320322772","display_name":"Funda\u00e7\u00e3o Arauc\u00e1ria","ror":"https://ror.org/02r7nkw81"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W1597700183","https://openalex.org/W1966535662","https://openalex.org/W1969545404","https://openalex.org/W1970001989","https://openalex.org/W1979654055","https://openalex.org/W1981944197","https://openalex.org/W1989121669","https://openalex.org/W1992627933","https://openalex.org/W1992941868","https://openalex.org/W1995358042","https://openalex.org/W2001024311","https://openalex.org/W2007032224","https://openalex.org/W2011232312","https://openalex.org/W2012886830","https://openalex.org/W2014171178","https://openalex.org/W2018527007","https://openalex.org/W2019882257","https://openalex.org/W2023301105","https://openalex.org/W2023542822","https://openalex.org/W2038683990","https://openalex.org/W2042567026","https://openalex.org/W2049094266","https://openalex.org/W2051026540","https://openalex.org/W2054087451","https://openalex.org/W2061079050","https://openalex.org/W2063186913","https://openalex.org/W2063722149","https://openalex.org/W2064348786","https://openalex.org/W2068654455","https://openalex.org/W2074718504","https://openalex.org/W2088779465","https://openalex.org/W2106265232","https://openalex.org/W2127464980","https://openalex.org/W2128004971","https://openalex.org/W2169525530","https://openalex.org/W2180756086","https://openalex.org/W2227150130","https://openalex.org/W2470863987","https://openalex.org/W2949599846","https://openalex.org/W2963459580"],"related_works":["https://openalex.org/W1514481392","https://openalex.org/W2147599942","https://openalex.org/W4322770021","https://openalex.org/W2971149938","https://openalex.org/W2020502833","https://openalex.org/W2244793131","https://openalex.org/W3203194254","https://openalex.org/W4280648077","https://openalex.org/W3016736150","https://openalex.org/W4300850840"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,29],"concerned":[3],"with":[4,16,23,36,93],"the":[5,8,13,20,58,74,78,94],"study":[6],"of":[7,12,34,69,77,96],"uniform":[9],"decay":[10],"rates":[11],"energy":[14],"associated":[15],"mixed":[17],"problems":[18],"involving":[19],"wave":[21],"equation":[22],"nonlinear":[24],"localized":[25],"damping.":[26],"The":[27],"domain":[28],"an":[30,41],"unbounded":[31,42],"open":[32],"set":[33],"$\\mathbb{R}^2$":[35],"finite":[37],"measure":[38],"and":[39,54,61],"has":[40],"smooth":[43],"boundary":[44,63],"$\\Gamma=\\Gamma_N":[45],"\\cup":[46],"\\Gamma_D$":[47],"such":[48],"that":[49],"$\\overline{\\Gamma}_N\\cap":[50],"\\overline{\\Gamma}_D\\neq\\emptyset$.":[51],"On":[52],"$\\Gamma_D$":[53],"$\\Gamma_N$":[55],"we":[56,72],"place":[57],"homogeneous":[59],"Dirichlet":[60],"Neumann":[62],"conditions,":[64],"respectively.":[65],"Due":[66],"to":[67],"lack":[68],"local":[70],"regularity,":[71],"used":[73],"elliptic":[75],"decomposition":[76],"solution":[79],"as":[80],"did":[81],"Grisvard":[82],"[J.":[83],"Math.":[84],"Pures":[85],"Appl.":[86],"(9),":[87],"68":[88],"(1989),":[89],"pp.":[90],"215--259]":[91],"combined":[92],"use":[95],"appropriated":[97],"cutoff":[98],"functions.":[99]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}