{"id":"https://openalex.org/W2896570293","doi":"https://doi.org/10.1137/17m1135645","title":"Global Cauchy Problem of a System of Parabolic Conservation Laws Arising From a Keller--Segel Type Chemotaxis Model","display_name":"Global Cauchy Problem of a System of Parabolic Conservation Laws Arising From a Keller--Segel Type Chemotaxis Model","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2896570293","doi":"https://doi.org/10.1137/17m1135645","mag":"2896570293"},"language":"en","primary_location":{"id":"doi:10.1137/17m1135645","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1135645","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/A5102843293","display_name":"Neng Zhu","orcid":"https://orcid.org/0009-0003-3517-6663"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Neng Zhu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111220210","display_name":"Zhengrong Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhengrong Liu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024441710","display_name":"Vincent R. Martinez","orcid":"https://orcid.org/0000-0003-1417-4223"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vincent R. Martinez","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5013659878","display_name":"Kun Zhao","orcid":"https://orcid.org/0000-0001-5059-9814"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kun Zhao","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5102843293"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5336,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.64708958,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"50","issue":"5","first_page":"5380","last_page":"5425"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T13234","display_name":"advanced mathematical theories","score":0.9682999849319458,"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"}},{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9667999744415283,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7715763449668884},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5666619539260864},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.56281578540802},{"id":"https://openalex.org/keywords/thermal-diffusivity","display_name":"Thermal diffusivity","score":0.5588433742523193},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.5419948101043701},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5417400598526001},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5384343266487122},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.5205698609352112},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.517915666103363},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.5152931213378906},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5000739097595215},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4834102392196655},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.4636225998401642},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4315493404865265},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.429458349943161},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.27315348386764526},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21847587823867798},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.1174665093421936},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09367445111274719}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7715763449668884},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5666619539260864},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.56281578540802},{"id":"https://openalex.org/C37668627","wikidata":"https://www.wikidata.org/wiki/Q3381809","display_name":"Thermal diffusivity","level":2,"score":0.5588433742523193},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.5419948101043701},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5417400598526001},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5384343266487122},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.5205698609352112},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.517915666103363},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.5152931213378906},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5000739097595215},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4834102392196655},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4636225998401642},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4315493404865265},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.429458349943161},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27315348386764526},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21847587823867798},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.1174665093421936},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09367445111274719},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/17m1135645","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1135645","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":[{"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15","score":0.75}],"awards":[{"id":"https://openalex.org/G6075914221","display_name":null,"funder_award_id":"201606150051","funder_id":"https://openalex.org/F4320322725","funder_display_name":"China Scholarship Council"},{"id":"https://openalex.org/G6087361762","display_name":null,"funder_award_id":"LEQSF(2015-18)-RD-A-24","funder_id":"https://openalex.org/F4320309392","funder_display_name":"Louisiana Board of Regents"},{"id":"https://openalex.org/G6239403255","display_name":null,"funder_award_id":"11571116","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7232912999","display_name":null,"funder_award_id":"413028","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"}],"funders":[{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"},{"id":"https://openalex.org/F4320309392","display_name":"Louisiana Board of Regents","ror":"https://ror.org/00jv89z46"},{"id":"https://openalex.org/F4320310142","display_name":"Tulane University","ror":"https://ror.org/04vmvtb21"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"},{"id":"https://openalex.org/F4320322792","display_name":"Nanchang University","ror":"https://ror.org/042v6xz23"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1977698389","https://openalex.org/W1978941072","https://openalex.org/W1982068953","https://openalex.org/W1983294494","https://openalex.org/W1997585819","https://openalex.org/W2002790950","https://openalex.org/W2006798765","https://openalex.org/W2011487751","https://openalex.org/W2011804741","https://openalex.org/W2013792702","https://openalex.org/W2014026771","https://openalex.org/W2017970715","https://openalex.org/W2021117151","https://openalex.org/W2026520292","https://openalex.org/W2036246322","https://openalex.org/W2042892258","https://openalex.org/W2045622430","https://openalex.org/W2051849259","https://openalex.org/W2053439652","https://openalex.org/W2056202747","https://openalex.org/W2080329728","https://openalex.org/W2090093951","https://openalex.org/W2111764281","https://openalex.org/W2126703430","https://openalex.org/W2161029367","https://openalex.org/W2195359973","https://openalex.org/W2316881268","https://openalex.org/W2328737802","https://openalex.org/W2488766299","https://openalex.org/W2517117478","https://openalex.org/W3022347268","https://openalex.org/W3098758841"],"related_works":["https://openalex.org/W2385382668","https://openalex.org/W2283102826","https://openalex.org/W2023596821","https://openalex.org/W2351460627","https://openalex.org/W2100701926","https://openalex.org/W1974236007","https://openalex.org/W1969098006","https://openalex.org/W3012869132","https://openalex.org/W1974759277","https://openalex.org/W2992019820"],"abstract_inverted_index":{"We":[0],"study":[1,51],"the":[2,8,50,70,73,87,106,116,120,123,127,135,144],"qualitative":[3],"behavior":[4],"of":[5,11,17,52,62,75,79,105,108,122,130,139,150],"solutions":[6,114,151],"to":[7,57,115],"Cauchy":[9,117],"problem":[10],"a":[12,32,58],"coupled":[13],"system":[14,29],"in":[15,21,69],"$(p,q)$":[16],"parabolic":[18],"conservation":[19],"laws":[20],"one":[22],"space":[23],"dimension":[24],"posed":[25],"on":[26,126],"$\\mathbb{R}$.":[27],"This":[28],"arises":[30],"from":[31],"Keller--Segel":[33],"type":[34],"repulsive":[35],"model":[36],"for":[37],"chemotaxis":[38],"with":[39],"singular":[40],"sensitivity":[41],"and":[42,96,119,132,143],"nonlinear":[43,59],"production":[44,60],"rate.":[45],"In":[46],"particular,":[47],"we":[48],"initiate":[49],"such":[53],"models":[54],"that":[55,103],"correspond":[56],"rate":[61],"$g(p)":[63],"=":[64],"p^\\gamma$,":[65],"where":[66,82],"$\\gamma":[67],">1$,":[68],"regime":[71],"when":[72],"ratio":[74],"chemical-to-cell":[76],"diffusivity":[77],"is":[78,101],"order":[80],"$\\varepsilon$,":[81],"$\\varepsilon":[83],">":[84],"0$":[85],"denotes":[86],"chemical":[88,146],"diffusion":[89,147],"coefficient.":[90],"By":[91],"assuming":[92],"$H^1$":[93],"initial":[94,109],"data":[95],"utilizing":[97],"energy":[98],"methods,":[99],"it":[100],"shown":[102],"regardless":[104],"magnitude":[107],"data,":[110],"there":[111],"exist":[112],"global-in-time":[113],"problem,":[118],"regularity":[121],"solution":[124],"depends":[125],"specific":[128],"values":[129],"$\\gamma$":[131],"$\\varepsilon$.":[133],"Moreover,":[134],"global":[136],"asymptotic":[137],"stability":[138],"constant":[140],"ground":[141],"states":[142],"zero":[145],"limit":[148],"($\\varepsilon\\to0$)":[149],"are":[152],"investigated.":[153]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3}],"updated_date":"2026-03-31T07:56:22.981413","created_date":"2025-10-10T00:00:00"}