{"id":"https://openalex.org/W2953554952","doi":"https://doi.org/10.1137/18m1226683","title":"Analysis of the Zero Relaxation Limit of Hyperbolic Balance Laws with Random Initial Data","display_name":"Analysis of the Zero Relaxation Limit of Hyperbolic Balance Laws with Random Initial Data","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2953554952","doi":"https://doi.org/10.1137/18m1226683","mag":"2953554952"},"language":"en","primary_location":{"id":"doi:10.1137/18m1226683","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1226683","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.osti.gov/biblio/1559614","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001242261","display_name":"James M. Scott","orcid":"https://orcid.org/0000-0001-7415-9506"},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"James M. Scott","raw_affiliation_strings":["Univ. of Tennessee, Knoxville, TN (United States)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. of Tennessee, Knoxville, TN (United States)","institution_ids":["https://openalex.org/I75027704"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031556606","display_name":"M. Paul Laiu","orcid":null},"institutions":[{"id":"https://openalex.org/I1289243028","display_name":"Oak Ridge National Laboratory","ror":"https://ror.org/01qz5mb56","country_code":"US","type":"facility","lineage":["https://openalex.org/I1289243028","https://openalex.org/I1330989302","https://openalex.org/I39565521","https://openalex.org/I4210159294"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. Paul Laiu","raw_affiliation_strings":["Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)","institution_ids":["https://openalex.org/I1289243028"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005248564","display_name":"Cory D. Hauck","orcid":"https://orcid.org/0000-0001-5559-502X"},"institutions":[{"id":"https://openalex.org/I1289243028","display_name":"Oak Ridge National Laboratory","ror":"https://ror.org/01qz5mb56","country_code":"US","type":"facility","lineage":["https://openalex.org/I1289243028","https://openalex.org/I1330989302","https://openalex.org/I39565521","https://openalex.org/I4210159294"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cory D. Hauck","raw_affiliation_strings":["Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)","institution_ids":["https://openalex.org/I1289243028"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5001242261"],"corresponding_institution_ids":["https://openalex.org/I75027704"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10401298,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"7","issue":"3","first_page":"806","last_page":"837"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9544000029563904,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9544000029563904,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9368000030517578,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9254999756813049,"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/mathematics","display_name":"Mathematics","score":0.7255285978317261},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.7000674605369568},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6819030046463013},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.6494529247283936},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.5949004292488098},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.5567705035209656},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5258277654647827},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49971699714660645},{"id":"https://openalex.org/keywords/weak-convergence","display_name":"Weak convergence","score":0.493566632270813},{"id":"https://openalex.org/keywords/limit-of-a-function","display_name":"Limit of a function","score":0.4585966169834137},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4469986855983734},{"id":"https://openalex.org/keywords/balance","display_name":"Balance (ability)","score":0.4430930018424988},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.083242267370224}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7255285978317261},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.7000674605369568},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6819030046463013},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.6494529247283936},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5949004292488098},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.5567705035209656},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5258277654647827},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49971699714660645},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.493566632270813},{"id":"https://openalex.org/C19448537","wikidata":"https://www.wikidata.org/wiki/Q33540","display_name":"Limit of a function","level":3,"score":0.4585966169834137},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4469986855983734},{"id":"https://openalex.org/C168031717","wikidata":"https://www.wikidata.org/wiki/Q1530280","display_name":"Balance (ability)","level":2,"score":0.4430930018424988},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.083242267370224},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C76178495","wikidata":"https://www.wikidata.org/wiki/Q4808784","display_name":"Asset (computer security)","level":2,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C99508421","wikidata":"https://www.wikidata.org/wiki/Q2678675","display_name":"Physical medicine and rehabilitation","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/18m1226683","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1226683","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},{"id":"pmh:oai:osti.gov:1559614","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1559614","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:osti.gov:1559614","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1559614","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1967117214","https://openalex.org/W1983156129","https://openalex.org/W1985198090","https://openalex.org/W1992812527","https://openalex.org/W1998135522","https://openalex.org/W2009546107","https://openalex.org/W2042241103","https://openalex.org/W2051247278","https://openalex.org/W2058362163","https://openalex.org/W2067207246","https://openalex.org/W2069366742","https://openalex.org/W2072014671","https://openalex.org/W2073447845","https://openalex.org/W2083845086","https://openalex.org/W2085168250","https://openalex.org/W2093522111","https://openalex.org/W2335312197"],"related_works":["https://openalex.org/W2121543990","https://openalex.org/W1973564655","https://openalex.org/W3004947349","https://openalex.org/W3039845694","https://openalex.org/W3099584520","https://openalex.org/W113523463","https://openalex.org/W1983994706","https://openalex.org/W4243589460","https://openalex.org/W3100534893","https://openalex.org/W2074974193"],"abstract_inverted_index":{"We":[0,73],"show":[1],"the":[2,5,29,34,53,59,63,70,76,82,85,88,92,101],"convergence":[3,54,102],"of":[4,9,14,28,62,78,84,90],"zero":[6],"relaxation":[7,35],"limit":[8,80],"$2":[10],"\\times":[11],"2$":[12],"systems":[13],"hyperbolic":[15,131],"balance":[16,132],"laws":[17,133],"with":[18,105,134],"stochastic":[19],"initial":[20,41],"data.":[21],"Precisely,":[22],"solutions":[23],"converge":[24],"to":[25,38,45],"a":[26,107,117],"solution":[27],"local":[30],"equilibrium":[31,96],"approximation":[32,97],"as":[33,116,127],"time":[36],"tends":[37],"zero.":[39],"The":[40],"data":[42],"are":[43],"assumed":[44],"depend":[46],"on":[47,110],"finitely":[48],"many":[49],"random":[50],"variables,":[51],"and":[52,94,100],"is":[55,98,103],"then":[56],"proved":[57],"via":[58],"appropriate":[60],"analogues":[61],"compensated":[64],"compactness":[65],"methods":[66],"used":[67,126],"in":[68,81],"treating":[69],"deterministic":[71],"case.":[72],"also":[74],"demonstrate":[75],"validity":[77],"this":[79,113],"case":[83],"semilinear":[86],"$p$-system;":[87],"well-posedness":[89],"both":[91],"system":[93],"its":[95],"proved,":[99],"shown":[104],"no":[106],"priori":[108],"conditions":[109],"solutions.":[111],"Here,":[112],"model":[114],"serves":[115],"prototype":[118],"for":[119,130],"understanding":[120],"how":[121],"asymptotic":[122],"approximations":[123],"can":[124],"be":[125],"control":[128],"variates":[129],"uncertainty.":[135]},"counts_by_year":[],"updated_date":"2026-05-03T08:25:01.440150","created_date":"2025-10-10T00:00:00"}