{"id":"https://openalex.org/W2996426817","doi":"https://doi.org/10.1137/18m1235922","title":"Particle Dynamics Subject to Impenetrable Boundaries: Existence and Uniqueness of Mild Solutions","display_name":"Particle Dynamics Subject to Impenetrable Boundaries: Existence and Uniqueness of Mild Solutions","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2996426817","doi":"https://doi.org/10.1137/18m1235922","mag":"2996426817"},"language":"en","primary_location":{"id":"doi:10.1137/18m1235922","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1235922","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067347406","display_name":"Masato Kimura","orcid":"https://orcid.org/0000-0001-6612-1954"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Masato Kimura","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020202776","display_name":"Patrick Meurs","orcid":"https://orcid.org/0000-0001-8184-5061"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Patrick van Meurs","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5108730997","display_name":"Zhenxing Yang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhenxing Yang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.66,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.72431233,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"51","issue":"6","first_page":"5049","last_page":"5076"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11500","display_name":"Evacuation and Crowd Dynamics","score":0.9905999898910522,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean 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/T11500","display_name":"Evacuation and Crowd Dynamics","score":0.9905999898910522,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean 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/T12677","display_name":"Sports Dynamics and Biomechanics","score":0.9884999990463257,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9652000069618225,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.8182691335678101},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7496732473373413},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7180044651031494},{"id":"https://openalex.org/keywords/particle-system","display_name":"Particle system","score":0.6701887249946594},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.6619636416435242},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.6335975527763367},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5196548700332642},{"id":"https://openalex.org/keywords/particle","display_name":"Particle (ecology)","score":0.454163134098053},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.44237205386161804},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.43101251125335693},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.42980748414993286},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4223533868789673},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34370458126068115},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1119222342967987},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08131811022758484}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.8182691335678101},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7496732473373413},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7180044651031494},{"id":"https://openalex.org/C179003449","wikidata":"https://www.wikidata.org/wiki/Q1757458","display_name":"Particle system","level":2,"score":0.6701887249946594},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.6619636416435242},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.6335975527763367},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5196548700332642},{"id":"https://openalex.org/C2778517922","wikidata":"https://www.wikidata.org/wiki/Q7140482","display_name":"Particle (ecology)","level":2,"score":0.454163134098053},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.44237205386161804},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.43101251125335693},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.42980748414993286},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4223533868789673},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34370458126068115},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1119222342967987},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08131811022758484},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C111368507","wikidata":"https://www.wikidata.org/wiki/Q43518","display_name":"Oceanography","level":1,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/18m1235922","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1235922","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G182160187","display_name":null,"funder_award_id":"JP17H02857","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G2092244807","display_name":null,"funder_award_id":"JP16H02155","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1820991953","https://openalex.org/W1971702124","https://openalex.org/W1977708050","https://openalex.org/W1980938760","https://openalex.org/W1985088055","https://openalex.org/W1987043692","https://openalex.org/W1987570505","https://openalex.org/W2007044713","https://openalex.org/W2050510300","https://openalex.org/W2051676758","https://openalex.org/W2062774474","https://openalex.org/W2068635707","https://openalex.org/W2080977367","https://openalex.org/W2093990123","https://openalex.org/W2095881925","https://openalex.org/W2168414272","https://openalex.org/W2240307629","https://openalex.org/W2606232181","https://openalex.org/W2950892036","https://openalex.org/W2964039363","https://openalex.org/W2980853146","https://openalex.org/W3021622851","https://openalex.org/W3105061012","https://openalex.org/W3124029185"],"related_works":["https://openalex.org/W2371448224","https://openalex.org/W3134495997","https://openalex.org/W2363680170","https://openalex.org/W2376428685","https://openalex.org/W4256082577","https://openalex.org/W2024346620","https://openalex.org/W2390277234","https://openalex.org/W4241530481","https://openalex.org/W3103060237","https://openalex.org/W2007838349"],"abstract_inverted_index":{"We":[0,122],"consider":[1,26],"the":[2,9,23,34,37,52,72,105,157],"dynamics":[3,39],"of":[4,55,87,93,104,126,135,150],"interacting":[5,136],"particle":[6,38,137],"systems":[7],"where":[8],"particles":[10,21],"are":[11,107],"confined":[12],"to":[13,51,64,109,132],"a":[14,44,58,115,140],"bounded,":[15],"possibly":[16],"nonconvex":[17],"domain":[18,159],"$\\Omega$.":[19,160],"When":[20],"hit":[22],"boundary,":[24],"we":[25,79],"an":[27,41,49,130],"instant":[28],"change":[29],"in":[30,77],"velocity,":[31],"which":[32],"turns":[33],"system":[35,59],"describing":[36],"into":[40],"ODE":[42],"with":[43,66,129,139],"discontinuous":[45],"right-hand":[46,68],"side.":[47],"As":[48],"alternative":[50],"typical":[53],"approach":[54],"analyzing":[56],"such":[57,94],"by":[60,75,148],"using":[61],"weak":[62],"solutions":[63,89,95,106,128],"ODEs":[65],"multivalued":[67],"sides":[69],"(i.e.,":[70],"applying":[71],"theory":[73,125],"introduced":[74],"Filippov":[76],"1988),":[78],"define":[80],"and":[81,111,144],"construct":[82],"mild":[83,88,127],"solutions.":[84],"The":[85],"merit":[86],"is":[90],"that":[91,101,112],"uniqueness":[92],"follows":[96],"easily":[97],"from":[98],"Gronwall's":[99],"lemma,":[100],"certain":[102],"properties":[103],"easy":[108],"establish,":[110],"they":[113],"provide":[114],"convenient":[116],"framework":[117],"for":[118,156],"proving":[119],"many-particle":[120],"limits.":[121],"supplement":[123],"our":[124],"application":[131],"gradient":[133],"flows":[134],"energies":[138],"singular":[141],"interaction":[142],"potential":[143],"illustrate":[145],"its":[146],"features":[147],"means":[149],"numerical":[151],"simulations":[152],"on":[153],"various":[154],"choices":[155],"(nonconvex)":[158]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}