{"id":"https://openalex.org/W2109905291","doi":"https://doi.org/10.1137/s0363012901394607","title":"Controllability of the Semilinear Parabolic Equation Governed by a Multiplicative Control in the Reaction Term: A Qualitative Approach","display_name":"Controllability of the Semilinear Parabolic Equation Governed by a Multiplicative Control in the Reaction Term: A Qualitative Approach","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2109905291","doi":"https://doi.org/10.1137/s0363012901394607","mag":"2109905291"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012901394607","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012901394607","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/A5112321447","display_name":"Alexander Y. Khapalov","orcid":null},"institutions":[{"id":"https://openalex.org/I72951846","display_name":"Washington State University","ror":"https://ror.org/05dk0ce17","country_code":"US","type":"education","lineage":["https://openalex.org/I72951846"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"A. Y. Khapalov","raw_affiliation_strings":["Dept. of Math., Washington State Univ., Pullman, WA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Math., Washington State Univ., Pullman, WA, USA","institution_ids":["https://openalex.org/I72951846"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5112321447"],"corresponding_institution_ids":["https://openalex.org/I72951846"],"apc_list":null,"apc_paid":null,"fwci":7.1296,"has_fulltext":false,"cited_by_count":66,"citation_normalized_percentile":{"value":0.96059034,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"41","issue":"6","first_page":"1886","last_page":"1900"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.965499997138977,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.9607999920845032,"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":0.8504844903945923},{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.8377475738525391},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.7219226360321045},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.6726711392402649},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6315157413482666},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.6142884492874146},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5925981998443604},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.5899147987365723},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.5606901049613953},{"id":"https://openalex.org/keywords/heat-equation","display_name":"Heat equation","score":0.5064107179641724},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4809103012084961},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.418127179145813},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41250079870224},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3783065676689148}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8504844903945923},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.8377475738525391},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.7219226360321045},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.6726711392402649},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6315157413482666},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.6142884492874146},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5925981998443604},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.5899147987365723},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.5606901049613953},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.5064107179641724},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4809103012084961},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.418127179145813},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41250079870224},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3783065676689148},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0363012901394607","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012901394607","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":16,"referenced_works":["https://openalex.org/W29191813","https://openalex.org/W630764638","https://openalex.org/W1574639858","https://openalex.org/W1967083369","https://openalex.org/W1967967021","https://openalex.org/W1973697519","https://openalex.org/W2009698203","https://openalex.org/W2059487456","https://openalex.org/W2069634773","https://openalex.org/W2114304162","https://openalex.org/W2121552308","https://openalex.org/W2123046091","https://openalex.org/W2152055417","https://openalex.org/W2160624683","https://openalex.org/W2170684215","https://openalex.org/W2334095483"],"related_works":["https://openalex.org/W4226345076","https://openalex.org/W4376635472","https://openalex.org/W2898193662","https://openalex.org/W1561764658","https://openalex.org/W1483125260","https://openalex.org/W2231621093","https://openalex.org/W3205884024","https://openalex.org/W2160720137","https://openalex.org/W45208602","https://openalex.org/W2109905291"],"abstract_inverted_index":{"In":[0],"this":[1,95],"paper":[2],"we":[3],"are":[4],"concerned":[5],"with":[6,20,97],"the":[7,37,46,87,91,124,132,135,141],"global":[8],"\"nonnegative\"":[9],"approximate":[10],"controllability":[11,88],"property":[12],"of":[13,90,94,123,131,134,143],"a":[14,25,32,144],"rather":[15],"general":[16],"semilinear":[17],"heat":[18],"equation":[19],"superlinear":[21],"term,":[22],"governed":[23],"in":[24,36,55,78],"bounded":[26],"domain":[27],"$\\Omega":[28],"\\subset":[29],"R^n$":[30],"by":[31,68],"multiplicative":[33],"(bilinear)":[34],"control":[35],"reaction":[38,129],"term":[39,99],"like":[40,100],"vu":[41],"(x,t),":[42],"where":[43,105],"v":[44],"is":[45,82,107,110],"control.":[47],"We":[48],"show":[49],"that":[50],"any":[51,63],"nonnegative":[52],"target":[53],"state":[54,67],"$L^2":[56],"(\\Omega)$":[57],"can":[58],"approximately":[59],"be":[60],"reached":[61],"from":[62],"nonnegative,":[64],"nonzero":[65],"initial":[66],"applying":[69],"at":[70,137],"most":[71],"three":[72],"static":[73],"bilinear":[74,98],"$L^\\infty":[75],"(\\Omega)$-controls":[76],"subsequently":[77],"time.":[79],"This":[80],"result":[81],"further":[83],"applied":[84],"to":[85,118],"discuss":[86],"properties":[89],"nonhomogeneous":[92],"version":[93],"problem":[96],"$v":[101],"(u":[102],"(x,t)-\\theta":[103],"(x))$,":[104],"$\\theta$":[106],"given.":[108],"Ourapproach":[109],"based":[111],"on":[112],"an":[113],"asymptotic":[114],"technique":[115],"allowing":[116],"us":[117],"distinguish":[119],"and":[120],"make":[121],"use":[122],"pure":[125,128],"diffusion":[126],"and/or":[127],"parts":[130],"dynamics":[133],"system":[136],"hand,":[138],"while":[139],"suppressing":[140],"effect":[142],"(general)":[145],"nonlinear":[146],"term.":[147]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-08-25T07:29:55.448023","created_date":"2025-10-10T00:00:00"}
