{"id":"https://openalex.org/W1975118867","doi":"https://doi.org/10.1137/s0036139996314106","title":"On the Spectral Properties and Stabilization of Acoustic Flow","display_name":"On the Spectral Properties and Stabilization of Acoustic Flow","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W1975118867","doi":"https://doi.org/10.1137/s0036139996314106","mag":"1975118867"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139996314106","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139996314106","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":true,"oa_status":"green","oa_url":"https://conservancy.umn.edu/bitstreams/a8605042-bd32-458e-94e9-73250eea91ef/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5115587783","display_name":"\u0411\u043e \u041b\u044e","orcid":"https://orcid.org/0000-0003-3045-628X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bo Liu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5028372683","display_name":"Walter Littman","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Walter Littman","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5115587783"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.927,"has_fulltext":true,"cited_by_count":56,"citation_normalized_percentile":{"value":0.93545129,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"59","issue":"1","first_page":"17","last_page":"34"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9994000196456909,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9993000030517578,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9980999827384949,"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":0.7015678882598877},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.6498047709465027},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.5700389742851257},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.5614386200904846},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.5570423007011414},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4851973354816437},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.46457868814468384},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.4218834936618805},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3627154529094696},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2875065207481384},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.14546102285385132}],"concepts":[{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.7015678882598877},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6498047709465027},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.5700389742851257},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.5614386200904846},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.5570423007011414},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4851973354816437},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.46457868814468384},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.4218834936618805},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3627154529094696},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2875065207481384},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.14546102285385132}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036139996314106","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139996314106","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"},{"id":"pmh:oai:conservancy.umn.edu:11299/2997","is_oa":true,"landing_page_url":"http://purl.umn.edu/2997","pdf_url":"https://conservancy.umn.edu/bitstreams/a8605042-bd32-458e-94e9-73250eea91ef/download","source":{"id":"https://openalex.org/S4306402521","display_name":"University of Minnesota Digital Conservancy (University of Minnesota)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130238516","host_organization_name":"University of Minnesota","host_organization_lineage":["https://openalex.org/I130238516"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"pmh:oai:conservancy.umn.edu:11299/2997","is_oa":true,"landing_page_url":"http://purl.umn.edu/2997","pdf_url":"https://conservancy.umn.edu/bitstreams/a8605042-bd32-458e-94e9-73250eea91ef/download","source":{"id":"https://openalex.org/S4306402521","display_name":"University of Minnesota Digital Conservancy (University of Minnesota)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130238516","host_organization_name":"University of Minnesota","host_organization_lineage":["https://openalex.org/I130238516"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},"sustainable_development_goals":[{"score":0.8100000023841858,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1975118867.pdf","grobid_xml":"https://content.openalex.org/works/W1975118867.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W560409768","https://openalex.org/W586747568","https://openalex.org/W1557040331","https://openalex.org/W1575147392","https://openalex.org/W1985600447","https://openalex.org/W1986566558","https://openalex.org/W2005722356","https://openalex.org/W2031639541","https://openalex.org/W2348508522","https://openalex.org/W4244700848","https://openalex.org/W4253840677"],"related_works":["https://openalex.org/W238609530","https://openalex.org/W2734192830","https://openalex.org/W3016395638","https://openalex.org/W1636163329","https://openalex.org/W4292947165","https://openalex.org/W3045121788","https://openalex.org/W3201655533","https://openalex.org/W3134442314","https://openalex.org/W2184770394","https://openalex.org/W2033341479"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"use":[4],"perturbation":[5],"theory":[6],"to":[7,106],"study":[8],"the":[9,73,78,84,91,103],"spectral":[10],"properties":[11],"and":[12,31,44,58,70,108],"energy":[13,104],"decay":[14],"of":[15,81,83,87],"two-dimensional":[16],"acoustic":[17],"flow":[18],"(cf.":[19],"[J.T.":[20],"Beale,":[21],"Indiana":[22],"Univ.":[23],"Math.":[24],"J.,":[25],"25":[26],"(1976),":[27],"pp.895--917],":[28],"[P.M.":[29],"Morse":[30],"K.U.":[32],"Ingard,":[33],"Theoretical":[34],"Acoustics,":[35],"McGraw-Hill,":[36],"New":[37],"York,":[38],"1968]):$\\phi_{tt}-c^2\\Delta":[39],"\\phi=0$":[40],"in":[41,56],"$\\Omega\\times(0,\\infty)$,":[42],"$m\\delta_{tt}+d\\delta_t+k\\delta=-\\rho\\phi_t$":[43],"$\\phi_x=\\delta_t$":[45],"on":[46,49,61,77],"$\\Gamma_0\\times(0,\\infty)$,":[47],"$\\frac{\\partial\\phi}{\\partial\\nu}=0$":[48],"$\\Gamma_1\\times(0,\\infty)$":[50],"with":[51,90],"initial":[52,115],"data":[53,116],"$\\phi(0)=\\phi_0,\\":[54],"\\phi_t(0)=\\phi_1$":[55],"$\\Omega$":[57],"$\\delta(0)=\\delta_0,\\":[59],"\\delta_t(0)=\\delta_1$":[60],"$\\Gamma_0$,":[62],"where":[63],"$\\Omega=(0,1)\\times":[64],"(0,1)$,":[65],"$\\Gamma_0=\\{(1,y);":[66],"\\0<y":[67],"<1\\}$,":[68],"$\\Gamma_1=\\partial\\Omega\\setminus\\Gamma_0$,":[69],"$\\nu$":[71],"is":[72,100],"external":[74],"normal":[75],"direction":[76],"boundary.":[79],"Locations":[80],"eigenvalues":[82],"infinitesimal":[85],"generator":[86],"semigroup":[88],"associated":[89],"above":[92],"system":[93],"are":[94,120],"estimated.":[95],"A":[96],"certain":[97,118],"\"Fourier\"":[98],"expansion":[99],"obtained.":[101],"That":[102],"decays":[105],"zero":[107],"like":[109,112],"t-1":[110],"(even":[111],"$t^{-\\beta}$)":[113],"if":[114],"satisfy":[117],"smoothness":[119],"proved.":[121]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}