{"id":"https://openalex.org/W2001024311","doi":"https://doi.org/10.1137/s036301290139107x","title":"Escape Function Conditions for the Observation, Control, and Stabilization of the Wave Equation","display_name":"Escape Function Conditions for the Observation, Control, and Stabilization of the Wave Equation","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2001024311","doi":"https://doi.org/10.1137/s036301290139107x","mag":"2001024311"},"language":"en","primary_location":{"id":"doi:10.1137/s036301290139107x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s036301290139107x","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/A5112580561","display_name":"Luc Miller","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Luc Miller","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5112580561"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.5463,"has_fulltext":false,"cited_by_count":62,"citation_normalized_percentile":{"value":0.88343909,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"41","issue":"5","first_page":"1554","last_page":"1566"},"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":0.9943000078201294,"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":0.9843999743461609,"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":0.8393710255622864},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.7650841474533081},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.6153687238693237},{"id":"https://openalex.org/keywords/cotangent-bundle","display_name":"Cotangent bundle","score":0.5457680225372314},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5424119234085083},{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.47111108899116516},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4394156336784363},{"id":"https://openalex.org/keywords/unit-sphere","display_name":"Unit sphere","score":0.42674359679222107},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34854012727737427},{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"Trigonometric functions","score":0.2879599928855896},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09018844366073608}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8393710255622864},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.7650841474533081},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.6153687238693237},{"id":"https://openalex.org/C7979169","wikidata":"https://www.wikidata.org/wiki/Q1142143","display_name":"Cotangent bundle","level":3,"score":0.5457680225372314},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5424119234085083},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.47111108899116516},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4394156336784363},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.42674359679222107},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34854012727737427},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.2879599928855896},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09018844366073608},{"id":"https://openalex.org/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s036301290139107x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s036301290139107x","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W630764638","https://openalex.org/W1137184376","https://openalex.org/W1514431383","https://openalex.org/W1966913165","https://openalex.org/W1969545404","https://openalex.org/W1992197114","https://openalex.org/W1992304430","https://openalex.org/W1992627933","https://openalex.org/W1995358042","https://openalex.org/W2009961626","https://openalex.org/W2014171178","https://openalex.org/W2031521898","https://openalex.org/W2034542160","https://openalex.org/W2037868571","https://openalex.org/W2069453797","https://openalex.org/W2080668001","https://openalex.org/W2080742168","https://openalex.org/W2087574051","https://openalex.org/W2121579066","https://openalex.org/W2152583013","https://openalex.org/W2174333115","https://openalex.org/W2470863987","https://openalex.org/W4241640491"],"related_works":["https://openalex.org/W2050687193","https://openalex.org/W3100725344","https://openalex.org/W2171443429","https://openalex.org/W2022843365","https://openalex.org/W4386399581","https://openalex.org/W2138969708","https://openalex.org/W2265407006","https://openalex.org/W2225422433","https://openalex.org/W2374152991","https://openalex.org/W3207745281"],"abstract_inverted_index":{"For":[0],"the":[1,18,47,84,89,150],"linear":[2],"wave":[3],"equation":[4],"with":[5,15,138],"time-invariant":[6],"coefficients":[7,118],"on":[8,46],"a":[9,60,79],"connected":[10],"compact":[11],"Riemannian":[12],"manifold":[13],"$(\\Omega,g)$":[14],"$C^{3}$":[16],"boundary,":[17],"geodesics":[19,85],"condition":[20,62,77,86],"of":[21,38,132],"Bardos,":[22],"Lebeau,":[23],"and":[24,119],"Rauch":[25],"[SIAM":[26],"J.":[27],"Control":[28],"Optim.,":[29],"30":[30],"(1992),":[31],"pp.":[32],"1024--1065]":[33],"is":[34,64],"characterized":[35],"in":[36,88,129,136],"terms":[37],"escape":[39,57,75],"functions,":[40],"which":[41,63],"are":[42],"some":[43,107,130],"Lyapunov":[44],"functions":[45,58],"phase":[48],"space":[49],"$S^{*}\\bar{\\Omega}$":[50],"(the":[51],"unit":[52],"sphere":[53],"cotangent":[54],"bundle).":[55],"Differentiable":[56],"yield":[59],"sufficient":[61],"slightly":[65],"less":[66],"sharp":[67],"but":[68],"does":[69],"not":[70],"refer":[71],"to":[72,105,116,127],"geodesics.":[73],"The":[74],"function":[76],"yields":[78],"straightforward":[80],"geometric":[81],"proof":[82],"that":[83,141],"holds":[87],"situations":[90,134],"where":[91],"first":[92,143],"order":[93,121,144],"differential":[94,145],"multiplier":[95,114,146],"methods":[96],"apply.":[97],"Using":[98],"microlocal":[99],"control":[100,108,152,155],"results,":[101],"it":[102],"allows":[103,125],"us":[104,126],"generalize":[106],"results":[109],"(that":[110],"were":[111],"obtained":[112],"by":[113],"methods)":[115],"variable":[117],"lower":[120],"terms.":[122],"It":[123],"also":[124],"prove,":[128],"class":[131],"simple":[133],"(e.g.,":[135],"$\\mathbb{R}^{2}$":[137],"constant":[139],"coefficients),":[140],"no":[142],"method":[147],"can":[148],"reach":[149],"optimal":[151],"time":[153],"or":[154],"regions.":[156]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":8},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}