{"id":"https://openalex.org/W2166119705","doi":"https://doi.org/10.1080/00207170701280895","title":"Boundary feedback stabilization of homogeneous equilibria in unstable fluid mixtures","display_name":"Boundary feedback stabilization of homogeneous equilibria in unstable fluid mixtures","publication_year":2007,"publication_date":"2007-06-01","ids":{"openalex":"https://openalex.org/W2166119705","doi":"https://doi.org/10.1080/00207170701280895","mag":"2166119705"},"language":"en","primary_location":{"id":"doi:10.1080/00207170701280895","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207170701280895","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","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/A5100380184","display_name":"Wenjun Liu","orcid":"https://orcid.org/0009-0008-4339-8043"},"institutions":[{"id":"https://openalex.org/I32038505","display_name":"University of Central Arkansas","ror":"https://ror.org/029bp0k25","country_code":"US","type":"education","lineage":["https://openalex.org/I32038505"]},{"id":"https://openalex.org/I4210152127","display_name":"Conway School of Landscape Design","ror":"https://ror.org/04q7y8a54","country_code":"US","type":"education","lineage":["https://openalex.org/I4210152127"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"W. Liu","raw_affiliation_strings":["Department of Mathematics , University of Central Arkansas , 201 Donaghey Avenue, Conway, AR 72035, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Central Arkansas , 201 Donaghey Avenue, Conway, AR 72035, USA","institution_ids":["https://openalex.org/I32038505","https://openalex.org/I4210152127"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018293076","display_name":"Miroslav Krsti\u0107","orcid":"https://orcid.org/0000-0002-5523-941X"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. Krstic","raw_affiliation_strings":["Dept of Mechanical and Aerospace Engineering , University of California , San Diego, La Jolla, CA 92093-0411, USA"],"affiliations":[{"raw_affiliation_string":"Dept of Mechanical and Aerospace Engineering , University of California , San Diego, La Jolla, CA 92093-0411, USA","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100380184"],"corresponding_institution_ids":["https://openalex.org/I32038505","https://openalex.org/I4210152127"],"apc_list":null,"apc_paid":null,"fwci":1.7419,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.88669641,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"80","issue":"6","first_page":"982","last_page":"989"},"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":0.9991000294685364,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/backstepping","display_name":"Backstepping","score":0.6620818376541138},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.6208034753799438},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.6163821220397949},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5982867479324341},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5216377377510071},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4795098602771759},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.4686676263809204},{"id":"https://openalex.org/keywords/feedback-control","display_name":"Feedback control","score":0.46733248233795166},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.4648773670196533},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4444041848182678},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4105822443962097},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3318716883659363},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.27579590678215027},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.19093933701515198},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.18243733048439026},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.16421127319335938},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1333005726337433},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13289815187454224}],"concepts":[{"id":"https://openalex.org/C72218879","wikidata":"https://www.wikidata.org/wiki/Q4839759","display_name":"Backstepping","level":4,"score":0.6620818376541138},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6208034753799438},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.6163821220397949},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5982867479324341},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5216377377510071},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4795098602771759},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.4686676263809204},{"id":"https://openalex.org/C3018651601","wikidata":"https://www.wikidata.org/wiki/Q183635","display_name":"Feedback control","level":2,"score":0.46733248233795166},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.4648773670196533},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4444041848182678},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4105822443962097},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3318716883659363},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.27579590678215027},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.19093933701515198},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.18243733048439026},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.16421127319335938},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1333005726337433},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13289815187454224},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207170701280895","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207170701280895","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W598774488","https://openalex.org/W1965339858","https://openalex.org/W1966249877","https://openalex.org/W1966922258","https://openalex.org/W1979390443","https://openalex.org/W1981440013","https://openalex.org/W1984255878","https://openalex.org/W1996344212","https://openalex.org/W1996850280","https://openalex.org/W2005136965","https://openalex.org/W2021722965","https://openalex.org/W2023785747","https://openalex.org/W2032947605","https://openalex.org/W2039844680","https://openalex.org/W2049483462","https://openalex.org/W2053336042","https://openalex.org/W2057388861","https://openalex.org/W2072675762","https://openalex.org/W2077764904","https://openalex.org/W2079545658","https://openalex.org/W2108536914","https://openalex.org/W2108850641","https://openalex.org/W2109775392","https://openalex.org/W2119967247","https://openalex.org/W2121855948","https://openalex.org/W2157153906","https://openalex.org/W2169319898","https://openalex.org/W2499036319","https://openalex.org/W2524339820","https://openalex.org/W2565022091","https://openalex.org/W2913727986","https://openalex.org/W3021722416","https://openalex.org/W3159390434","https://openalex.org/W3160857725","https://openalex.org/W4241651000"],"related_works":["https://openalex.org/W2771027241","https://openalex.org/W1765905465","https://openalex.org/W2793080664","https://openalex.org/W2186140227","https://openalex.org/W2132535444","https://openalex.org/W2534185822","https://openalex.org/W2367651125","https://openalex.org/W2387936656","https://openalex.org/W2063297487","https://openalex.org/W2567073787"],"abstract_inverted_index":{"We":[0,23,43],"consider":[1],"the":[2,31,36,51,59,67,74],"problem":[3],"of":[4,8],"boundary":[5,25,54],"feedback":[6,26,55],"stabilization":[7],"homogeneous":[9,75],"equilibria":[10],"in":[11],"unstable":[12,19],"fluid":[13],"mixtures":[14],"that":[15],"are":[16],"governed":[17],"by":[18],"linear":[20],"reaction-convection-diffusion":[21],"equations.":[22],"extend":[24],"control":[27],"laws":[28],"designed":[29],"for":[30,61,66],"one-dimensional":[32,62],"reaction-diffusion":[33],"equation":[34],"using":[35],"backstepping":[37],"method":[38],"to":[39,58],"this":[40],"higher-dimensional":[41],"case.":[42],"show":[44],"that,":[45],"under":[46],"certain":[47],"mathematical":[48],"conditions":[49],"on":[50],"velocity":[52],"field,":[53],"controls":[56],"similar":[57],"ones":[60],"equations":[63],"also":[64],"works":[65],"higher":[68],"dimensional":[69],"case":[70],"and":[71],"exponentially":[72],"stabilize":[73],"equilibrium":[76],"zero":[77],"at":[78],"any":[79],"given":[80],"decay":[81],"rate.":[82]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}