{"id":"https://openalex.org/W2073415286","doi":"https://doi.org/10.1137/s0363012998341411","title":"Minimax Control of Parabolic Systems with State Constraints","display_name":"Minimax Control of Parabolic Systems with State Constraints","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2073415286","doi":"https://doi.org/10.1137/s0363012998341411","mag":"2073415286"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012998341411","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012998341411","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/A5086528835","display_name":"Nadir Arada","orcid":"https://orcid.org/0000-0002-0958-7931"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nadir Arada","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5110346346","display_name":"Jean\u2010Pierre Raymond","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jean-Pierre Raymond","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5086528835"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.86595687,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.93141843,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"38","issue":"1","first_page":"254","last_page":"271"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9973000288009644,"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"}},"topics":[{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9973000288009644,"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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9973000288009644,"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":0.9972000122070312,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.8937718868255615},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8627592325210571},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.8494640588760376},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.837812602519989},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.6001128554344177},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.46366479992866516},{"id":"https://openalex.org/keywords/compactification","display_name":"Compactification (mathematics)","score":0.4512457549571991},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4256015121936798},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4150570034980774},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40300872921943665},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2842322885990143},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25013962388038635},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08651307225227356}],"concepts":[{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.8937718868255615},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8627592325210571},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.8494640588760376},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.837812602519989},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.6001128554344177},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.46366479992866516},{"id":"https://openalex.org/C2779165322","wikidata":"https://www.wikidata.org/wiki/Q546145","display_name":"Compactification (mathematics)","level":2,"score":0.4512457549571991},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4256015121936798},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4150570034980774},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40300872921943665},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2842322885990143},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25013962388038635},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08651307225227356},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0363012998341411","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012998341411","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W64850344","https://openalex.org/W958319805","https://openalex.org/W1528796636","https://openalex.org/W1584259498","https://openalex.org/W1968980197","https://openalex.org/W1996088437","https://openalex.org/W1999530275","https://openalex.org/W2016408881","https://openalex.org/W2040888244","https://openalex.org/W2091080063","https://openalex.org/W2103284380","https://openalex.org/W2167924593"],"related_works":["https://openalex.org/W2140020064","https://openalex.org/W143502885","https://openalex.org/W42113618","https://openalex.org/W2103468410","https://openalex.org/W1856228368","https://openalex.org/W3197542402","https://openalex.org/W2971527398","https://openalex.org/W1972598260","https://openalex.org/W2043909370","https://openalex.org/W4309320703"],"abstract_inverted_index":{"In":[0],"this":[1,58],"paper":[2],"we":[3,60],"study":[4],"a":[5,25,30,62],"minimax":[6,21],"control":[7],"problem":[8],"for":[9],"parabolic":[10],"equations":[11],"in":[12,51,76,84],"the":[13,36,43,77,85],"presence":[14],"of":[15,35,40,53],"pointwise":[16],"state":[17,81,88],"constraints.":[18,89],"The":[19,32],"terminology":[20],"here":[22],"refers":[23],"to":[24],"cost":[26],"functional":[27],"defined":[28],"with":[29,79,87],"$L^{\\infty}$-norm.":[31],"directional":[33],"derivatives":[34],"$L^{\\infty}$-norm":[37],"are":[38,73,97],"elements":[39],"$(L^{\\infty})'$.":[41],"Therefore,":[42],"adjoint":[44],"equation":[45],"may":[46],"involve":[47],"finitely":[48],"additive":[49],"measures":[50],"place":[52],"Radon":[54],"measures.":[55],"To":[56],"overcome":[57],"difficulty,":[59],"introduce":[61],"compactification":[63],"(of":[64],"Stone--\\u{C}ech":[65],"type).":[66],"We":[67],"prove":[68],"necessary":[69],"optimality":[70,95],"conditions":[71,96],"which":[72],"new,":[74],"both":[75],"case":[78,86],"no":[80],"constraints":[82],"and":[83],"Under":[90],"some":[91],"convexity":[92],"conditions,":[93],"these":[94],"also":[98],"sufficient.":[99]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}