{"id":"https://openalex.org/W46353859","doi":"https://doi.org/10.1007/978-3-642-36062-6_8","title":"On Existence, Uniqueness, and Convergence of Optimal Control Problems Governed by Parabolic Variational Inequalities","display_name":"On Existence, Uniqueness, and Convergence of Optimal Control Problems Governed by Parabolic Variational Inequalities","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W46353859","doi":"https://doi.org/10.1007/978-3-642-36062-6_8","mag":"46353859"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-36062-6_8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-36062-6_8","pdf_url":null,"source":{"id":"https://openalex.org/S4210175514","display_name":"IFIP International Federation for Information Processing/IFIP","issn_l":"1571-5736","issn":["1571-5736","1861-2288"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP Advances in Information and Communication Technology","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://inria.hal.science/hal-01347525","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051121156","display_name":"Mahdi Boukrouche","orcid":"https://orcid.org/0000-0002-6333-3668"},"institutions":[{"id":"https://openalex.org/I86767153","display_name":"Universit\u00e9 Jean Monnet","ror":"https://ror.org/04yznqr36","country_code":"FR","type":"education","lineage":["https://openalex.org/I86767153"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I203339264","display_name":"Universit\u00e9 de Lyon","ror":"https://ror.org/01rk35k63","country_code":"FR","type":"education","lineage":["https://openalex.org/I203339264"]},{"id":"https://openalex.org/I4210104796","display_name":"Institut Camille Jordan","ror":"https://ror.org/01ekw7f87","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I112936343","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210104796","https://openalex.org/I4405259976","https://openalex.org/I48430043"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Mahdi Boukrouche","raw_affiliation_strings":["CNRS UMR 5208, ICJ, Lyon University UJM, F-42023, France","UJM - Universit\u00e9 Jean Monnet - Saint-\u00c9tienne (10, Rue Tr\u00e9filerie \u2013 CS 82301\r\n42023 Saint-\u00c9tienne Cedex 2 - France)"],"affiliations":[{"raw_affiliation_string":"CNRS UMR 5208, ICJ, Lyon University UJM, F-42023, France","institution_ids":["https://openalex.org/I203339264","https://openalex.org/I4210104796","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"UJM - Universit\u00e9 Jean Monnet - Saint-\u00c9tienne (10, Rue Tr\u00e9filerie \u2013 CS 82301\r\n42023 Saint-\u00c9tienne Cedex 2 - France)","institution_ids":["https://openalex.org/I86767153"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067406965","display_name":"Domingo A. Tarzia","orcid":"https://orcid.org/0000-0002-2813-0419"},"institutions":[{"id":"https://openalex.org/I151201029","display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas","ror":"https://ror.org/03cqe8w59","country_code":"AR","type":"government","lineage":["https://openalex.org/I151201029","https://openalex.org/I4210123736","https://openalex.org/I4387155568"]},{"id":"https://openalex.org/I204205638","display_name":"Austral University","ror":"https://ror.org/04043k259","country_code":"AR","type":"education","lineage":["https://openalex.org/I204205638"]}],"countries":["AR"],"is_corresponding":false,"raw_author_name":"Domingo A. Tarzia","raw_affiliation_strings":["CONICET and Austral University, Rosario, Argentina","Universidad Austral (Mariano Acosta 1611, B1630FHB Pilar, Buenos Aires - Argentina)","CONICET - Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas [Buenos Aires] (Avda. Rivadavia 1917 - CP C1033AAJ - Cdad. de Buenos Aires - Argentina)"],"affiliations":[{"raw_affiliation_string":"CONICET and Austral University, Rosario, Argentina","institution_ids":["https://openalex.org/I204205638"]},{"raw_affiliation_string":"Universidad Austral (Mariano Acosta 1611, B1630FHB Pilar, Buenos Aires - Argentina)","institution_ids":["https://openalex.org/I204205638"]},{"raw_affiliation_string":"CONICET - Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas [Buenos Aires] (Avda. Rivadavia 1917 - CP C1033AAJ - Cdad. de Buenos Aires - Argentina)","institution_ids":["https://openalex.org/I151201029"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5051121156"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I4210104796","https://openalex.org/I86767153"],"apc_list":null,"apc_paid":null,"fwci":0.3812,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.57231626,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"76","last_page":"84"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9998000264167786,"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":0.9998000264167786,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9983000159263611,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8322024345397949},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.8049314618110657},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.8015695810317993},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5742166042327881},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5585475564002991},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.53431236743927},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.5316097736358643},{"id":"https://openalex.org/keywords/maximum-principle","display_name":"Maximum principle","score":0.5206664800643921},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5112752914428711},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.49081477522850037},{"id":"https://openalex.org/keywords/obstacle-problem","display_name":"Obstacle problem","score":0.487781822681427},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41166049242019653},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2289905846118927}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8322024345397949},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.8049314618110657},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.8015695810317993},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5742166042327881},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5585475564002991},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.53431236743927},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.5316097736358643},{"id":"https://openalex.org/C31010330","wikidata":"https://www.wikidata.org/wiki/Q1914255","display_name":"Maximum principle","level":3,"score":0.5206664800643921},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5112752914428711},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.49081477522850037},{"id":"https://openalex.org/C132369183","wikidata":"https://www.wikidata.org/wiki/Q3406250","display_name":"Obstacle problem","level":3,"score":0.487781822681427},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41166049242019653},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2289905846118927},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-642-36062-6_8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-36062-6_8","pdf_url":null,"source":{"id":"https://openalex.org/S4210175514","display_name":"IFIP International Federation for Information Processing/IFIP","issn_l":"1571-5736","issn":["1571-5736","1861-2288"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP Advances in Information and Communication Technology","raw_type":"book-chapter"},{"id":"pmh:oai:HAL:hal-01347525v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01347525","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"25th System Modeling and Optimization (CSMO), Sep 2011, Berlin, Germany. pp.76-84, &#x27E8;10.1007/978-3-642-36062-6_8&#x27E9;","raw_type":"Conference papers"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01347525v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01347525","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"25th System Modeling and Optimization (CSMO), Sep 2011, Berlin, Germany. pp.76-84, &#x27E8;10.1007/978-3-642-36062-6_8&#x27E9;","raw_type":"Conference papers"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W25938444","https://openalex.org/W639940401","https://openalex.org/W1481206684","https://openalex.org/W1508622707","https://openalex.org/W1516681311","https://openalex.org/W1523612522","https://openalex.org/W1820125862","https://openalex.org/W1980816179","https://openalex.org/W1989789314","https://openalex.org/W1993608133","https://openalex.org/W2037092586","https://openalex.org/W2046369964","https://openalex.org/W2059586880","https://openalex.org/W2067986422","https://openalex.org/W2077145283","https://openalex.org/W2080682332","https://openalex.org/W2081385560","https://openalex.org/W2085903974","https://openalex.org/W2118168201","https://openalex.org/W4249851362"],"related_works":["https://openalex.org/W2275565576","https://openalex.org/W2951022852","https://openalex.org/W1996998222","https://openalex.org/W2066764892","https://openalex.org/W1989743438","https://openalex.org/W2041307625","https://openalex.org/W2616717838","https://openalex.org/W1967850176","https://openalex.org/W1518141773","https://openalex.org/W2949515281"],"abstract_inverted_index":{"I)":[0],"We":[1,38,82,135],"consider":[2,181],"a":[3,7,15,21,25,30,46,78,114,173,182,187,191,234,237,243,247,256,260],"system":[4,188,257],"governed":[5,189,258],"by":[6,190,259],"free":[8],"boundary":[9,19,67,80,175,241,251,279],"problem":[10,75,170,185,229],"with":[11,24,160],"Tresca":[12],"condition":[13],"on":[14,236],"part":[16,238],"of":[17,20,34,48,70,88,113,146,156,166,195,207,239,242,264],"the":[18,35,40,63,89,92,110,119,123,127,143,147,161,167,196,204,211,217,228,240,272,293],"material":[22,244],"domain":[23,245],"source":[26],"term":[27,125],"g":[28,54],"through":[29,118],"parabolic":[31,85,128,183,192,261],"variational":[32,86,98,129,193,262],"inequality":[33,94,130,263],"second":[36,90,265],"kind.":[37],"prove":[39],"existence":[41,273],"and":[42,69,107,150,214,274],"uniqueness":[43,213,275],"results":[44,206,276],"to":[45,62,77,153,164,172],"family":[47,155],"distributed":[49,72,219],"optimal":[50,73,148,157,168,220,252,280],"control":[51,74,158,169,221,248,253,281],"problems":[52,159,282],"over":[53],"for":[55,84,96,122,131,210,216,255,277,283],"each":[56,132,284],"parameter":[57,133,285],"h":[58,139,286,296],">":[59,287],"0,":[60,288],"associated":[61,76,152,171],"Newton":[64,162],"law":[65,163],"(Robin":[66],"condition),":[68],"another":[71],"Dirichlet":[79,174],"condition.":[81,176],"generalize":[83],"inequalities":[87,99,194],"kind":[91,198,266],"Mignot\u2019s":[93],"obtained":[95],"elliptic":[97],"(Mignot,":[100],"J.":[101],"Funct.":[102],"Anal.,":[103],"22":[104],"(1976),":[105],"130-185),":[106],"we":[108,180,200,225,268],"obtain":[109,203,271],"strictly":[111],"convexity":[112],"quadratic":[115],"cost":[116],"functional":[117],"regularization":[120],"method":[121],"non-differentiable":[124],"in":[126,227,231,290],"h.":[134],"also":[136,202,270],"prove,":[137],"when":[138,295],"\u2192":[140,297],"+":[141,298],"\u221e,":[142],"strong":[144],"convergence":[145,215,294],"controls":[149],"states":[151],"this":[154,291],"that":[165],"II)":[177],"Moreover,":[178],"if":[179],"obstacle":[184],"as":[186,246],"first":[197],"then":[199,267],"can":[201,269],"same":[205],"Part":[208,232],"I":[209],"existence,":[212],"corresponding":[218],"problems.":[222],"III)":[223],"If":[224],"consider,":[226],"given":[230],"I,":[233],"flux":[235],"variable":[249],"(Neumann":[250],"problem)":[254],"Neumann":[278],"but":[289],"case":[292],"\u221e":[299],"is":[300],"still":[301],"an":[302],"open":[303],"problem.":[304]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}
