{"id":"https://openalex.org/W1483681519","doi":"https://doi.org/10.1137/15m102424x","title":"Sliding Mode Control for a Nonlinear Phase-Field System","display_name":"Sliding Mode Control for a Nonlinear Phase-Field System","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W1483681519","doi":"https://doi.org/10.1137/15m102424x","mag":"1483681519"},"language":"en","primary_location":{"id":"doi:10.1137/15m102424x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m102424x","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1506.01665","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102862771","display_name":"Viorel Barbu","orcid":"https://orcid.org/0000-0002-4715-9778"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Viorel Barbu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048835991","display_name":"Pierluigi Colli","orcid":"https://orcid.org/0000-0002-7921-5041"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pierluigi Colli","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051522439","display_name":"Gianni Gilardi","orcid":"https://orcid.org/0000-0002-0651-4307"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gianni Gilardi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057343803","display_name":"Gabriela Marinoschi","orcid":"https://orcid.org/0000-0001-5887-1202"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gabriela Marinoschi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5017446516","display_name":"Elisabetta Rocca","orcid":"https://orcid.org/0000-0002-9930-907X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Elisabetta Rocca","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2041,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.48268079,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"55","issue":"3","first_page":"2108","last_page":"2133"},"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":0.9995999932289124,"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":0.9995999932289124,"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/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9829000234603882,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/control-theory","display_name":"Control theory (sociology)","score":0.682976484298706},{"id":"https://openalex.org/keywords/sliding-mode-control","display_name":"Sliding mode control","score":0.6630775332450867},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5287755727767944},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.5243906378746033},{"id":"https://openalex.org/keywords/variable-structure-control","display_name":"Variable structure control","score":0.5037638545036316},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.4964447617530823},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.49464938044548035},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49106788635253906},{"id":"https://openalex.org/keywords/mode","display_name":"Mode (computer interface)","score":0.4426645040512085},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4183712899684906},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.3948381543159485},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.3703356981277466},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2771624028682709},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24463799595832825},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.1490439772605896},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07090947031974792}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.682976484298706},{"id":"https://openalex.org/C36662352","wikidata":"https://www.wikidata.org/wiki/Q6008560","display_name":"Sliding mode control","level":3,"score":0.6630775332450867},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5287755727767944},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.5243906378746033},{"id":"https://openalex.org/C185109637","wikidata":"https://www.wikidata.org/wiki/Q7915740","display_name":"Variable structure control","level":4,"score":0.5037638545036316},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4964447617530823},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.49464938044548035},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49106788635253906},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.4426645040512085},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4183712899684906},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.3948381543159485},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3703356981277466},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2771624028682709},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24463799595832825},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.1490439772605896},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07090947031974792},{"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/15m102424x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m102424x","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"},{"id":"pmh:oai:arXiv.org:1506.01665","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1506.01665","pdf_url":"https://arxiv.org/pdf/1506.01665","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:1483681519","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1506.01665.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1506.01665","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1506.01665","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1506.01665","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1506.01665","pdf_url":"https://arxiv.org/pdf/1506.01665","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.7300000190734863}],"awards":[{"id":"https://openalex.org/G5361476978","display_name":null,"funder_award_id":"FP7-IDEAS-ERC-StG 256872","funder_id":"https://openalex.org/F4320334960","funder_display_name":"Seventh Framework Programme"},{"id":"https://openalex.org/G5652328398","display_name":null,"funder_award_id":"2010A2TFX2","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G6005772231","display_name":"Entropy formulation of evolutionary phase transitions","funder_award_id":"256872","funder_id":"https://openalex.org/F4320338352","funder_display_name":"FP7 Ideas: European Research Council"},{"id":"https://openalex.org/G8603592002","display_name":null,"funder_award_id":"PNII-ID-PCE-2011-3-0027","funder_id":"https://openalex.org/F4320323983","funder_display_name":"Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii"}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320321499","display_name":"Fondazione Cariplo","ror":"https://ror.org/01gb56c55"},{"id":"https://openalex.org/F4320321873","display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","ror":"https://ror.org/0166hxq48"},{"id":"https://openalex.org/F4320322651","display_name":"Consiglio Nazionale delle Ricerche","ror":"https://ror.org/04zaypm56"},{"id":"https://openalex.org/F4320323899","display_name":"Academia Rom\u00e2na","ror":"https://ror.org/0561n6946"},{"id":"https://openalex.org/F4320323983","display_name":"Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii","ror":"https://ror.org/01q7jq182"},{"id":"https://openalex.org/F4320326078","display_name":"Regione Lombardia","ror":null},{"id":"https://openalex.org/F4320333369","display_name":"Gruppo Nazionale per l'Analisi Matematica, la Probabilit\u00e0 e le loro Applicazioni","ror":null},{"id":"https://openalex.org/F4320334960","display_name":"Seventh Framework Programme","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320338352","display_name":"FP7 Ideas: European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1483681519.pdf","grobid_xml":"https://content.openalex.org/works/W1483681519.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1489222793","https://openalex.org/W1516447630","https://openalex.org/W1582617215","https://openalex.org/W1586161429","https://openalex.org/W1596635901","https://openalex.org/W1607530402","https://openalex.org/W1799659174","https://openalex.org/W1866311589","https://openalex.org/W1969944700","https://openalex.org/W1983753664","https://openalex.org/W1989314144","https://openalex.org/W1991245833","https://openalex.org/W2037913112","https://openalex.org/W2052058856","https://openalex.org/W2073078790","https://openalex.org/W2075043821","https://openalex.org/W2111141957","https://openalex.org/W2112609906","https://openalex.org/W2118772813","https://openalex.org/W2155312662","https://openalex.org/W2165902635","https://openalex.org/W2247602753","https://openalex.org/W2322956738","https://openalex.org/W2369386221","https://openalex.org/W2963301640","https://openalex.org/W2964092306"],"related_works":["https://openalex.org/W2964104012","https://openalex.org/W2792410700","https://openalex.org/W2173551325","https://openalex.org/W2283892691","https://openalex.org/W2068536430","https://openalex.org/W1497280145","https://openalex.org/W1994433363","https://openalex.org/W2537288191","https://openalex.org/W2105211672","https://openalex.org/W151545286","https://openalex.org/W2033364831","https://openalex.org/W148820847","https://openalex.org/W256553255","https://openalex.org/W2887037359","https://openalex.org/W2058462592","https://openalex.org/W1973592128","https://openalex.org/W2045217311","https://openalex.org/W3135231770","https://openalex.org/W2045289467","https://openalex.org/W2757054523"],"abstract_inverted_index":{"In":[0],"the":[1,4,22,29,36,44,49,56,67,88,93,103,106,116,124,129,137,145,153,168,171],"present":[2],"contribution":[3],"sliding":[5,57],"mode":[6],"control":[7,38,86,138],"(SMC)":[8],"problem":[9],"for":[10,28,144],"a":[11,71,99,110,132],"phase-field":[12,30],"model":[13],"of":[14,66,73,84,102,170],"Caginalp":[15],"type":[16,31],"is":[17,140,150],"considered.":[18],"First":[19],"we":[20,41,60],"prove":[21],"well-posedness":[23],"and":[24,97,105,118,127,162],"some":[25],"regularity":[26],"results":[27],"state":[32],"systems":[33],"modified":[34],"by":[35],"state-feedback":[37],"laws.":[39],"Then,":[40],"show":[42],"that":[43,64],"chosen":[45],"SMC":[46],"laws":[47],"force":[48],"system":[50],"to":[51,108],"reach":[52,109],"within":[53],"finite":[54],"time":[55,164],"manifold":[58],"(that":[59],"chose":[61],"in":[62,77,92,123,142,152],"order":[63],"one":[65,90],"physical":[68],"variables":[69],"or":[70],"combination":[72,101],"them":[74],"remains":[75],"constant":[76],"time).":[78],"We":[79],"study":[80],"three":[81],"different":[82],"types":[83],"feedback":[85],"laws:":[87],"first":[89,146],"appears":[91],"internal":[94],"energy":[95],"balance":[96],"forces":[98],"linear":[100],"temperature":[104],"phase":[107,125,130],"given":[111],"(space":[112],"dependent)":[113],"value,":[114],"while":[115],"second":[117],"third":[119,154],"ones":[120],"are":[121],"added":[122],"relation":[126],"lead":[128],"onto":[131],"prescribed":[133],"target":[134],"$\\phi^*$.":[135],"While":[136],"law":[139],"nonlocal":[141],"space":[143],"two":[147],"problems,":[148],"it":[149],"local":[151],"one,":[155],"i.e.,":[156],"its":[157],"value":[158,169],"at":[159],"any":[160,163],"point":[161],"just":[165],"depends":[166],"on":[167],"state.":[172]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}