{"id":"https://openalex.org/W2560286998","doi":"https://doi.org/10.1137/16m1106675","title":"Uniform Regularity for Linear Kinetic Equations with Random Input Based on Hypocoercivity","display_name":"Uniform Regularity for Linear Kinetic Equations with Random Input Based on Hypocoercivity","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2560286998","doi":"https://doi.org/10.1137/16m1106675","mag":"2560286998"},"language":"en","primary_location":{"id":"doi:10.1137/16m1106675","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1106675","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100438891","display_name":"Qin Li","orcid":"https://orcid.org/0000-0001-9210-8948"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Qin Li","raw_affiliation_strings":["University of Wisconsin"],"affiliations":[{"raw_affiliation_string":"University of Wisconsin","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100335932","display_name":"Li Wang","orcid":"https://orcid.org/0000-0002-0593-8175"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li Wang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100438891"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.8808,"has_fulltext":false,"cited_by_count":47,"citation_normalized_percentile":{"value":0.96610286,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"5","issue":"1","first_page":"1193","last_page":"1219"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9995999932289124,"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":0.9995999932289124,"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9995999932289124,"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/T11277","display_name":"Thermal properties of materials","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/randomness","display_name":"Randomness","score":0.8415980339050293},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6665294170379639},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5805490016937256},{"id":"https://openalex.org/keywords/boltzmann-equation","display_name":"Boltzmann equation","score":0.5691067576408386},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5434513092041016},{"id":"https://openalex.org/keywords/kinetic-energy","display_name":"Kinetic energy","score":0.48837822675704956},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4751291573047638},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.4590406119823456},{"id":"https://openalex.org/keywords/random-field","display_name":"Random field","score":0.44238007068634033},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4190391004085541},{"id":"https://openalex.org/keywords/collision","display_name":"Collision","score":0.4144722521305084},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3372056484222412},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2086348831653595},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1663895845413208},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.14295491576194763},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09834444522857666}],"concepts":[{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.8415980339050293},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6665294170379639},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5805490016937256},{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.5691067576408386},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5434513092041016},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.48837822675704956},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4751291573047638},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4590406119823456},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.44238007068634033},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4190391004085541},{"id":"https://openalex.org/C121704057","wikidata":"https://www.wikidata.org/wiki/Q352070","display_name":"Collision","level":2,"score":0.4144722521305084},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3372056484222412},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2086348831653595},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1663895845413208},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.14295491576194763},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09834444522857666},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m1106675","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1106675","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3444760245","display_name":null,"funder_award_id":"DMS-1619778","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G7976605019","display_name":null,"funder_award_id":"DMS-1620135","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"}],"funders":[{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W1967562270","https://openalex.org/W1971642223","https://openalex.org/W1977657887","https://openalex.org/W1982421072","https://openalex.org/W1983156129","https://openalex.org/W2012205310","https://openalex.org/W2015036110","https://openalex.org/W2018159038","https://openalex.org/W2019579692","https://openalex.org/W2027564485","https://openalex.org/W2033018963","https://openalex.org/W2036766781","https://openalex.org/W2037635208","https://openalex.org/W2041509689","https://openalex.org/W2044147726","https://openalex.org/W2048791667","https://openalex.org/W2049222546","https://openalex.org/W2055460625","https://openalex.org/W2056518217","https://openalex.org/W2063334232","https://openalex.org/W2083845086","https://openalex.org/W2083974861","https://openalex.org/W2086140935","https://openalex.org/W2090385746","https://openalex.org/W2094168343","https://openalex.org/W2132254595","https://openalex.org/W2135329423","https://openalex.org/W2136602340","https://openalex.org/W2143591652","https://openalex.org/W2163715525","https://openalex.org/W2168418390","https://openalex.org/W2217218176","https://openalex.org/W2303941511","https://openalex.org/W2562640896","https://openalex.org/W2575736835","https://openalex.org/W2600269031","https://openalex.org/W2765696110","https://openalex.org/W2963066768","https://openalex.org/W2963196150","https://openalex.org/W3021293439","https://openalex.org/W4244321008"],"related_works":["https://openalex.org/W3034924094","https://openalex.org/W2981906196","https://openalex.org/W3094954546","https://openalex.org/W1513698804","https://openalex.org/W4310560702","https://openalex.org/W2029712093","https://openalex.org/W1982811510","https://openalex.org/W3161859090","https://openalex.org/W2007632118","https://openalex.org/W2394261629"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"study":[4],"the":[5,20,23,28,34,49,55,59,62,66,70,72,83,87,92,99,114,118,123,126,130,141],"effect":[6],"of":[7,22,36,58,65,117,122,146],"randomness":[8],"in":[9,18,44,75,103,125,132,143],"kinetic":[10,147],"equations":[11],"that":[12],"preserve":[13],"mass.":[14],"Our":[15],"focus":[16],"is":[17,41,74,78,134],"proving":[19],"analyticity":[21],"solution":[24,124],"with":[25,48],"respect":[26],"to":[27,33],"randomness,":[29],"which":[30],"naturally":[31],"leads":[32],"convergence":[35,131],"numerical":[37,154],"methods.":[38],"The":[39,110],"analysis":[40,145],"carried":[42],"out":[43],"a":[45],"general":[46],"setting,":[47],"regularity":[50],"result":[51],"not":[52],"depending":[53],"on":[54,113,137],"specific":[56],"form":[57],"collision":[60],"term,":[61],"probability":[63],"distribution":[64],"random":[67,127],"variables,":[68],"or":[69],"regime":[71],"system":[73],"and":[76,91,98,106,129],"thereby":[77],"termed":[79],"\u201cuniform.\"":[80],"Applications":[81],"include":[82],"linear":[84],"Boltzmann":[85],"equation,":[86],"Bhatnagar--Gross--Krook":[88],"(BGK)":[89],"model,":[90,94],"Carlemann":[93],"among":[95],"many":[96],"others,":[97],"results":[100],"hold":[101],"true":[102],"kinetic,":[104],"parabolic,":[105],"high":[107,119],"field":[108],"regimes.":[109],"proof":[111],"relies":[112],"explicit":[115],"expression":[116],"order":[120],"derivatives":[121],"space,":[128],"time":[133],"mainly":[135],"based":[136],"hypocoercivity,":[138],"which,":[139],"despite":[140],"popularity":[142],"PDE":[144],"theory,":[148],"has":[149],"rarely":[150],"been":[151],"used":[152],"for":[153],"algorithms.":[155]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":5}],"updated_date":"2026-04-22T08:38:42.863108","created_date":"2025-10-10T00:00:00"}
