{"id":"https://openalex.org/W2143621779","doi":"https://doi.org/10.1109/cdc.2008.4738861","title":"Sensitivity analysis and computational uncertainty with applications to control of nonlinear parabolic partial differential equations","display_name":"Sensitivity analysis and computational uncertainty with applications to control of nonlinear parabolic partial differential equations","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2143621779","doi":"https://doi.org/10.1109/cdc.2008.4738861","mag":"2143621779"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2008.4738861","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2008.4738861","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 47th IEEE Conference on Decision and Control","raw_type":"proceedings-article"},"type":"conference-paper","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/A5102791907","display_name":"John A. Burns","orcid":"https://orcid.org/0000-0003-1840-927X"},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John A. Burns","raw_affiliation_strings":["Interdisciplinary Center for Applied Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA","Interdiscipl. Center for Appl. Math., Virginia Polytech. Inst. & State Univ., Blacksburg, VA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Interdisciplinary Center for Applied Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA","institution_ids":["https://openalex.org/I859038795"]},{"raw_affiliation_string":"Interdiscipl. Center for Appl. Math., Virginia Polytech. Inst. & State Univ., Blacksburg, VA, USA","institution_ids":["https://openalex.org/I859038795"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113684947","display_name":"Lisa G. Davis","orcid":null},"institutions":[{"id":"https://openalex.org/I23732399","display_name":"Montana State University","ror":"https://ror.org/02w0trx84","country_code":"US","type":"education","lineage":["https://openalex.org/I23732399","https://openalex.org/I4210126032"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lisa G. Davis","raw_affiliation_strings":["Department of Mathematical Sciences, Montana State University, Bozemon, MT, USA","Dept. of Math. Sci., Montana State Univ., Bozeman, MT, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Montana State University, Bozemon, MT, USA","institution_ids":["https://openalex.org/I23732399"]},{"raw_affiliation_string":"Dept. of Math. Sci., Montana State Univ., Bozeman, MT, USA","institution_ids":["https://openalex.org/I23732399"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.30347054,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"143","issue":null,"first_page":"3989","last_page":"3994"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9944000244140625,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9714999794960022,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.8345727324485779},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6891342401504517},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6698576807975769},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.6635533571243286},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.6261013746261597},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.5420786142349243},{"id":"https://openalex.org/keywords/numerical-partial-differential-equations","display_name":"Numerical partial differential equations","score":0.5287575125694275},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4708064794540405},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46928489208221436},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4576195478439331},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4122791886329651},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3664940893650055},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30001506209373474},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.25815024971961975},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15226757526397705},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.08680710196495056},{"id":"https://openalex.org/keywords/electronic-engineering","display_name":"Electronic engineering","score":0.07791832089424133},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.05931922793388367}],"concepts":[{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.8345727324485779},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6891342401504517},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6698576807975769},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.6635533571243286},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.6261013746261597},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.5420786142349243},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"score":0.5287575125694275},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4708064794540405},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46928489208221436},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4576195478439331},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4122791886329651},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3664940893650055},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30001506209373474},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25815024971961975},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15226757526397705},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.08680710196495056},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.07791832089424133},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.05931922793388367},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cdc.2008.4738861","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2008.4738861","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 47th IEEE Conference on Decision and Control","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.418.5492","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.418.5492","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.vt.edu/people/burns/papers/Sensitivity analysis and computational uncertainty with applications to control of nonlinear parabolic partial differential equations_47_CDC_2008.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W52682513","https://openalex.org/W111535946","https://openalex.org/W243369316","https://openalex.org/W247481854","https://openalex.org/W1493195308","https://openalex.org/W1493694426","https://openalex.org/W1523615189","https://openalex.org/W1535429593","https://openalex.org/W1541939020","https://openalex.org/W1545654816","https://openalex.org/W1559539328","https://openalex.org/W1594759473","https://openalex.org/W1969747329","https://openalex.org/W1971896291","https://openalex.org/W1974163519","https://openalex.org/W1975446230","https://openalex.org/W1976574893","https://openalex.org/W1980210848","https://openalex.org/W2039195921","https://openalex.org/W2052136899","https://openalex.org/W2065676431","https://openalex.org/W2081268922","https://openalex.org/W2168568158","https://openalex.org/W2296992688","https://openalex.org/W2593856576"],"related_works":["https://openalex.org/W1967450583","https://openalex.org/W2066764747","https://openalex.org/W2385175414","https://openalex.org/W2083817219","https://openalex.org/W2264582182","https://openalex.org/W3047860677","https://openalex.org/W4399084239","https://openalex.org/W2343093002","https://openalex.org/W3131706438","https://openalex.org/W2969693569"],"abstract_inverted_index":{"In":[0,28],"this":[1],"paper":[2],"we":[3,30],"illustrate":[4,40],"how":[5,46],"sensitivities":[6,50],"can":[7],"be":[8],"used":[9],"to":[10,15,39,44,51],"provide":[11,36],"a":[12],"practical":[13],"precursor":[14],"dynamic":[16],"transitions":[17],"and":[18,35,43],"numerical":[19,37],"uncertainty":[20],"in":[21],"parameterized":[22],"nonlinear":[23],"parabolic":[24],"partial":[25],"differential":[26],"equations.":[27],"particular,":[29],"focus":[31],"on":[32],"reaction-diffusion":[33],"equations":[34],"examples":[38],"the":[41],"ideas":[42],"suggest":[45],"one":[47],"might":[48],"use":[49],"address":[52],"computational":[53],"uncertainty.":[54]},"counts_by_year":[],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}