{"id":"https://openalex.org/W4410428473","doi":"https://doi.org/10.1109/tac.2025.3570828","title":"Boundary Arc and Boundary Point Stabilization of Reaction-Diffusion Equations on the Unit Disk","display_name":"Boundary Arc and Boundary Point Stabilization of Reaction-Diffusion Equations on the Unit Disk","publication_year":2025,"publication_date":"2025-05-16","ids":{"openalex":"https://openalex.org/W4410428473","doi":"https://doi.org/10.1109/tac.2025.3570828"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2025.3570828","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2025.3570828","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic 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/A5022121143","display_name":"Arthur J. Krener","orcid":"https://orcid.org/0000-0002-5137-3726"},"institutions":[{"id":"https://openalex.org/I35364215","display_name":"Naval Postgraduate School","ror":"https://ror.org/033yfkj90","country_code":"US","type":"education","lineage":["https://openalex.org/I1330347796","https://openalex.org/I3130687028","https://openalex.org/I35364215"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Arthur J. Krener","raw_affiliation_strings":["Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA, USA","institution_ids":["https://openalex.org/I35364215"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5022121143"],"corresponding_institution_ids":["https://openalex.org/I35364215"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14158544,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"70","issue":"8","first_page":"5222","last_page":"5237"},"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":0.9976999759674072,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/boundary","display_name":"Boundary (topology)","score":0.6351216435432434},{"id":"https://openalex.org/keywords/arc","display_name":"Arc (geometry)","score":0.5286736488342285},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.5130102038383484},{"id":"https://openalex.org/keywords/unit-disk","display_name":"Unit disk","score":0.49500101804733276},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.44228172302246094},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4389439523220062},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40088748931884766},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33360564708709717},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.3299944996833801},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24102520942687988},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2065306007862091},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.14478367567062378}],"concepts":[{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6351216435432434},{"id":"https://openalex.org/C83415579","wikidata":"https://www.wikidata.org/wiki/Q161973","display_name":"Arc (geometry)","level":2,"score":0.5286736488342285},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.5130102038383484},{"id":"https://openalex.org/C47177299","wikidata":"https://www.wikidata.org/wiki/Q2390323","display_name":"Unit disk","level":2,"score":0.49500101804733276},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.44228172302246094},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4389439523220062},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40088748931884766},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33360564708709717},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.3299944996833801},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24102520942687988},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2065306007862091},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.14478367567062378}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2025.3570828","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2025.3570828","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8011907523","display_name":null,"funder_award_id":"FA9550-20-1-0318","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1501644353","https://openalex.org/W1966922258","https://openalex.org/W2085433634","https://openalex.org/W2321052409","https://openalex.org/W2415753819","https://openalex.org/W2499641798","https://openalex.org/W3118475267","https://openalex.org/W3159976593","https://openalex.org/W3208472047","https://openalex.org/W4376633210","https://openalex.org/W4402261806"],"related_works":["https://openalex.org/W2081283454","https://openalex.org/W2544839741","https://openalex.org/W1986614877","https://openalex.org/W2810064750","https://openalex.org/W4392388433","https://openalex.org/W1982796873","https://openalex.org/W4285791829","https://openalex.org/W2902861956","https://openalex.org/W2341351063","https://openalex.org/W2246092933"],"abstract_inverted_index":{"The":[0],"uncontrolled":[1],"diffusion":[2],"equation":[3,30,39,227],"on":[4,88,210,293],"the":[5,28,89,92,98,110,122,130,139,143,162,166,170,175,179,184,196,201,211],"unit":[6],"disk":[7,93],"under":[8],"homogeneous":[9],"Neumann":[10],"boundary":[11,67,71,75,90,126],"conditions":[12],"is":[13,19,112,121,161,237],"only":[14,276],"neutrally":[15,197],"stable":[16,198],"as":[17,129,214,283,285],"zero":[18,137],"an":[20,238,251],"eigenvalue.":[21],"If":[22],"we":[23,45,51,78,95,154],"add":[24],"linear":[25],"reaction":[26],"terms":[27],"resulting":[29],"can":[31,96,228,260,275,280,291],"be":[32,49,103,229,261,281],"unstable.":[33],"To":[34],"stabilize":[35],"such":[36],"a":[37,41,55,156,224,255],"reaction-diffusion":[38,226],"to":[40,48,102,136,147,243,263],"uniform":[42],"state":[43],"which":[44,236],"conveniently":[46],"take":[47,277,292],"zero,":[50],"pose":[52],"and":[53,70,94,183,296],"solve":[54],"Linear":[56],"Quadratic":[57],"Regulator":[58],"(LQR).":[59],"We":[60,172,190,220,248,267],"consider":[61],"two":[62,270],"types":[63],"of":[64,91,125,132,152,165,169,178,240,253],"control":[65,69,77,97,111,120,128,144,288],"actuation,":[66],"arc":[68,76,108,127,134],"point":[72,119],"control.":[73],"With":[74],"assume":[79],"that":[80,192,269,274,290],"there":[81],"are":[82,216],"<inline-formula":[83,113],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[84,114],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[85,115],"notation=\"LaTeX\">$m$</tex-math></inline-formula>":[86,116],"arcs":[87],"time":[99],"varying":[100],"flux":[101],"spatially":[104],"constant":[105],"across":[106],"each":[107,133,150],"so":[109],"dimensional.":[117],"Boundary":[118],"idealized":[123],"limit":[124],"length":[131],"shrinks":[135],"but":[138,206],"gain":[140],"factor":[141],"multiplying":[142],"inversely":[145],"goes":[146],"infinity.":[148],"For":[149],"type":[151],"actuation":[153],"derive":[155],"Riccati":[157],"PDE":[158],"whose":[159],"solution":[160],"Fredholm":[163,176],"kernel":[164,177],"optimal":[167,181,193],"cost":[168],"LQR.":[171],"also":[173,221],"compute":[174],"corresponding":[180],"feedback":[182,194],"first":[185],"few":[186],"closed":[187],"loop":[188],"eigenvalues.":[189],"show":[191,222,268],"moves":[195],"eigenvalue":[199],"into":[200],"open":[202],"left":[203],"half":[204],"plane":[205],"has":[207],"little":[208],"effect":[209],"other":[212],"eigenvalues":[213],"they":[215],"already":[217],"sufficiently":[218],"stable.":[219],"how":[223,254],"nonlinear":[225,244],"stabilized":[230,262],"by":[231],"nonLinear":[232],"nonQuadatic":[233],"Regulation":[234],"(nLnQR)":[235],"extension":[239],"Al'brekht's":[241],"method":[242],"distributed":[245,256],"parameter":[246],"systems.":[247],"close":[249],"with":[250],"example":[252],"predator":[257],"prey":[258],"system":[259],"its":[264],"equilibrium":[265],"point.":[266],"unilateral":[271],"controls":[272],"(controls":[273],"nonpositive":[278],"values)":[279],"almost":[282],"stabilizing":[284],"one":[286],"bilateral":[287],"(control":[289],"both":[294],"positive":[295],"negative":[297],"values).":[298]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
