{"id":"https://openalex.org/W3038211345","doi":"https://doi.org/10.1137/19m1263017","title":"Dissipation and Semigroup on $H^k_n$: Non-cutoff Linearized Boltzmann Operator with Soft Potential","display_name":"Dissipation and Semigroup on $H^k_n$: Non-cutoff Linearized Boltzmann Operator with Soft Potential","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3038211345","doi":"https://doi.org/10.1137/19m1263017","mag":"3038211345"},"language":"en","primary_location":{"id":"doi:10.1137/19m1263017","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1263017","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://scholars.cityu.edu.hk/en/publications/dissipation-and-semigroup-on-ihsupksupsubnsubi-non-cutoff-lineari","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073755636","display_name":"Dingqun Deng","orcid":"https://orcid.org/0000-0001-9678-314X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Dingqun Deng","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5073755636"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.2164,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.92555364,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"52","issue":"3","first_page":"3093","last_page":"3113"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9998999834060669,"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9988999962806702,"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/mathematics","display_name":"Mathematics","score":0.8023284673690796},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.6871688961982727},{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.6819096803665161},{"id":"https://openalex.org/keywords/cutoff","display_name":"Cutoff","score":0.5575602054595947},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5426308512687683},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4925745129585266},{"id":"https://openalex.org/keywords/dissipative-operator","display_name":"Dissipative operator","score":0.4750411808490753},{"id":"https://openalex.org/keywords/boltzmann-constant","display_name":"Boltzmann constant","score":0.41548678278923035},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3895091414451599},{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.27073514461517334},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1911536157131195},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.07946088910102844},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07357913255691528}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8023284673690796},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.6871688961982727},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.6819096803665161},{"id":"https://openalex.org/C2778217198","wikidata":"https://www.wikidata.org/wiki/Q556977","display_name":"Cutoff","level":2,"score":0.5575602054595947},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5426308512687683},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4925745129585266},{"id":"https://openalex.org/C101370240","wikidata":"https://www.wikidata.org/wiki/Q1229326","display_name":"Dissipative operator","level":3,"score":0.4750411808490753},{"id":"https://openalex.org/C35304006","wikidata":"https://www.wikidata.org/wiki/Q5962","display_name":"Boltzmann constant","level":2,"score":0.41548678278923035},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3895091414451599},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.27073514461517334},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1911536157131195},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.07946088910102844},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07357913255691528},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/19m1263017","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1263017","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"},{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/dissipation-and-semigroup-on-ihsupksupsubnsubi-non-cutoff-lineari","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:publications/7b19ebb9-bcb2-44ac-ac19-11844cd2a8bd","is_oa":true,"landing_page_url":"https://hdl.handle.net/2031/7b19ebb9-bcb2-44ac-ac19-11844cd2a8bd","pdf_url":null,"source":{"id":"https://openalex.org/S7407055387","display_name":"CityU Scholars","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"DENG, D 2020, 'DISSIPATION AND SEMIGROUP ON H k n : NON-CUTOFF LINEARIZED BOLTZMANN OPERATOR WITH SOFT POTENTIAL', SIAM Journal on Mathematical Analysis, vol. 52, no. 3, pp. 3093-3113. https://doi.org/10.1137/19M1263017","raw_type":"article"}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/dissipation-and-semigroup-on-ihsupksupsubnsubi-non-cutoff-lineari","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"No poverty","id":"https://metadata.un.org/sdg/1","score":0.46000000834465027},{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.4300000071525574}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W2002262989","https://openalex.org/W2007196946","https://openalex.org/W2023023275","https://openalex.org/W2036881335","https://openalex.org/W2045786831","https://openalex.org/W2229311954","https://openalex.org/W2963040471","https://openalex.org/W2963278106"],"related_works":["https://openalex.org/W3092388660","https://openalex.org/W1778838665","https://openalex.org/W2347486132","https://openalex.org/W3175879137","https://openalex.org/W2328322229","https://openalex.org/W2372927850","https://openalex.org/W2084331620","https://openalex.org/W2357421324","https://openalex.org/W110408122","https://openalex.org/W2091135737"],"abstract_inverted_index":{"In":[0,28],"this":[1],"paper,":[2],"we":[3],"find":[4],"that":[5],"the":[6,12,29,32,38,63],"linearized":[7],"collision":[8],"operator":[9],"$L$":[10],"of":[11,31,60,71],"non-cutoff":[13],"Boltzmann":[14,33],"equation":[15,34],"with":[16,26],"soft":[17],"potential":[18],"generates":[19],"a":[20,43,57],"strongly":[21],"continuous":[22],"semigroup":[23],"on":[24,50],"$H^k_n$,":[25],"$k,n\\in\\mathbb{R}$.":[27],"theory":[30],"without":[35],"angular":[36],"cutoff,":[37],"weighted":[39],"Sobolev":[40],"space":[41],"plays":[42],"fundamental":[44],"role.":[45],"The":[46],"proof":[47],"is":[48,73],"based":[49],"pseudodifferential":[51],"calculus,":[52],"and,":[53],"in":[54],"general,":[55],"for":[56],"specific":[58],"class":[59],"Weyl":[61],"quantization,":[62],"$L^2$":[64],"dissipation":[65],"implies":[66],"$H^k_n$":[67],"dissipation.":[68],"This":[69],"kind":[70],"estimate":[72],"also":[74],"known":[75],"as":[76],"G\u00e5rding's":[77],"inequality.":[78]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":7}],"updated_date":"2026-04-14T08:04:32.555800","created_date":"2025-10-10T00:00:00"}