{"id":"https://openalex.org/W2023782437","doi":"https://doi.org/10.1137/140977023","title":"Exponential Stabilization of the Wave Equation by Dirichlet Integral Feedback","display_name":"Exponential Stabilization of the Wave Equation by Dirichlet Integral Feedback","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2023782437","doi":"https://doi.org/10.1137/140977023","mag":"2023782437"},"language":"en","primary_location":{"id":"doi:10.1137/140977023","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140977023","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/A5073661737","display_name":"Martin Gugat","orcid":"https://orcid.org/0000-0002-5281-110X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Martin Gugat","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5073661737"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2608,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.83267175,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"53","issue":"1","first_page":"526","last_page":"546"},"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":0.9937000274658203,"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":0.988099992275238,"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":0.8453068733215332},{"id":"https://openalex.org/keywords/exponential-decay","display_name":"Exponential decay","score":0.617381751537323},{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.5899973511695862},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.5521928071975708},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.530020534992218},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.4781716465950012},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4608682096004486},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.4564509391784668},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4518794119358063},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.4337509870529175},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4274146854877472},{"id":"https://openalex.org/keywords/feedback-control","display_name":"Feedback control","score":0.4157543182373047},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.1979123055934906},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.1579861044883728},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12742263078689575},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0947655737400055}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8453068733215332},{"id":"https://openalex.org/C180188523","wikidata":"https://www.wikidata.org/wiki/Q574576","display_name":"Exponential decay","level":2,"score":0.617381751537323},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.5899973511695862},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.5521928071975708},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.530020534992218},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.4781716465950012},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4608682096004486},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4564509391784668},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4518794119358063},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4337509870529175},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4274146854877472},{"id":"https://openalex.org/C3018651601","wikidata":"https://www.wikidata.org/wiki/Q183635","display_name":"Feedback control","level":2,"score":0.4157543182373047},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.1979123055934906},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.1579861044883728},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12742263078689575},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0947655737400055},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/140977023","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140977023","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":"Affordable and clean energy","score":0.4399999976158142,"id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W118814629","https://openalex.org/W215223255","https://openalex.org/W1432340843","https://openalex.org/W1545761024","https://openalex.org/W1595090407","https://openalex.org/W1969363190","https://openalex.org/W1990834757","https://openalex.org/W1992471512","https://openalex.org/W1992907975","https://openalex.org/W1994730848","https://openalex.org/W2000753997","https://openalex.org/W2014884383","https://openalex.org/W2021983887","https://openalex.org/W2030036911","https://openalex.org/W2043966287","https://openalex.org/W2063186913","https://openalex.org/W2134431133","https://openalex.org/W4250608538","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2036697162","https://openalex.org/W2332386680","https://openalex.org/W2561315646","https://openalex.org/W2248621902","https://openalex.org/W2003779889","https://openalex.org/W3010940295","https://openalex.org/W2963749880","https://openalex.org/W390249267","https://openalex.org/W2620022550","https://openalex.org/W4300624503"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,23,36,42,61,79,83,102,125,161,178,188,194,206],"problem":[3],"of":[4,8,82,147,169,187,193,205],"boundary":[5,116],"feedback":[6,72,89,117,138,141,163,198],"stabilization":[7],"a":[9,70,95,114,120,148],"vibrating":[10],"string":[11],"that":[12,31,68,98,118,172],"is":[13,65,90,99],"fixed":[14],"at":[15,22],"one":[16],"end":[17],"and":[18,39,55,129,191],"with":[19,53,86,157,185],"control":[20],"action":[21],"other":[24],"end.":[25],"In":[26,109],"contrast":[27],"to":[28,92,101,144,166,174,202],"previous":[29],"studies":[30],"have":[32],"required":[33],"$L^2$-regularity":[34,192],"for":[35,41,50,69,74,135],"initial":[37,43,51,56,77,155,179,189,195],"position":[38,190],"$H^{-1}$-regularity":[40],"velocity,":[44,196],"in":[45,58,124],"this":[46,110,132,175],"paper":[47],"we":[48,112],"allow":[49],"positions":[52],"$L^1$-regularity":[54],"velocities":[57],"$W^{-1,1}$":[59],"on":[60],"space":[62],"interval.":[63],"It":[64],"well":[66],"known":[67],"certain":[71],"parameter,":[73],"sufficiently":[75],"regular":[76,154,184],"states":[78,156,180],"classical":[80,207],"energy":[81,171],"closed-loop":[84,122],"system":[85,123],"Neumann":[87],"velocity":[88],"controlled":[91],"zero":[93],"after":[94],"finite":[96],"time":[97,104],"equal":[100],"minimal":[103],"where":[105],"exact":[106],"controllability":[107],"holds.":[108],"paper,":[111],"present":[113],"Dirichlet":[115],"yields":[119],"well-defined":[121],"($L^1$,":[126],"$W^{-1,1}$)":[127],"framework":[128],"also":[130,200],"has":[131],"property.":[133],"Moreover,":[134],"all":[136],"positive":[137],"parameters":[139],"our":[140,197],"law":[142,164,199],"leads":[143,165,201],"exponential":[145,167,203],"decay":[146,168,204],"suitably":[149],"defined":[150],"$L^1$-energy.":[151],"For":[152],"more":[153,183],"$(L^2,":[158],"\\,H^{-1})$":[159],"regularity,":[160],"proposed":[162],"an":[170],"corresponds":[173],"framework.":[176],"If":[177],"are":[181],"even":[182],"$H^1$-regularity":[186],"energy.":[208]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-25T07:29:55.448023","created_date":"2025-10-10T00:00:00"}
