{"id":"https://openalex.org/W3093963048","doi":"https://doi.org/10.1137/19m1242823","title":"The Keller--Segel System on the Two-Dimensional-Hyperbolic Space","display_name":"The Keller--Segel System on the Two-Dimensional-Hyperbolic Space","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3093963048","doi":"https://doi.org/10.1137/19m1242823","mag":"3093963048"},"language":"en","primary_location":{"id":"doi:10.1137/19m1242823","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1242823","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/A5017218057","display_name":"Patrick Maheux","orcid":"https://orcid.org/0009-0006-1581-0200"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Patrick Maheux","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5012015569","display_name":"Vittoria Pierfelice","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vittoria Pierfelice","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5017218057"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0689,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.44780732,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"52","issue":"5","first_page":"5036","last_page":"5065"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9660999774932861,"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":0.9455999732017517,"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":0.8704737424850464},{"id":"https://openalex.org/keywords/hyperbolic-space","display_name":"Hyperbolic space","score":0.7296853065490723},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6158667206764221},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5926918983459473},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.5258311033248901},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5038794875144958},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.46087509393692017},{"id":"https://openalex.org/keywords/fujita-scale","display_name":"Fujita scale","score":0.4538766145706177},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.4458082616329193},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.43922606110572815},{"id":"https://openalex.org/keywords/hyperbolic-manifold","display_name":"Hyperbolic manifold","score":0.4327964782714844},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.43107470870018005},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.42433881759643555},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.4208011031150818},{"id":"https://openalex.org/keywords/h\u00f6lder-condition","display_name":"H\u00f6lder condition","score":0.4171209931373596},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.41523391008377075},{"id":"https://openalex.org/keywords/hyperbolic-function","display_name":"Hyperbolic function","score":0.2752295732498169},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1319272816181183}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8704737424850464},{"id":"https://openalex.org/C83677898","wikidata":"https://www.wikidata.org/wiki/Q1878538","display_name":"Hyperbolic space","level":2,"score":0.7296853065490723},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6158667206764221},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5926918983459473},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.5258311033248901},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5038794875144958},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.46087509393692017},{"id":"https://openalex.org/C22891489","wikidata":"https://www.wikidata.org/wiki/Q380770","display_name":"Fujita scale","level":2,"score":0.4538766145706177},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.4458082616329193},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.43922606110572815},{"id":"https://openalex.org/C70984080","wikidata":"https://www.wikidata.org/wiki/Q2619102","display_name":"Hyperbolic manifold","level":3,"score":0.4327964782714844},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.43107470870018005},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.42433881759643555},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.4208011031150818},{"id":"https://openalex.org/C553313952","wikidata":"https://www.wikidata.org/wiki/Q1537963","display_name":"H\u00f6lder condition","level":2,"score":0.4171209931373596},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.41523391008377075},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.2752295732498169},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1319272816181183},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1242823","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1242823","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W811003184","https://openalex.org/W1973692656","https://openalex.org/W1982945358","https://openalex.org/W1990598341","https://openalex.org/W1999441752","https://openalex.org/W2006329687","https://openalex.org/W2016897879","https://openalex.org/W2026979923","https://openalex.org/W2031088533","https://openalex.org/W2038366232","https://openalex.org/W2042892258","https://openalex.org/W2048026906","https://openalex.org/W2069398935","https://openalex.org/W2086255511","https://openalex.org/W2950854560","https://openalex.org/W2988378713"],"related_works":["https://openalex.org/W3128228318","https://openalex.org/W4240041676","https://openalex.org/W2045336066","https://openalex.org/W4297783881","https://openalex.org/W4366330423","https://openalex.org/W2016712750","https://openalex.org/W4388640056","https://openalex.org/W1608408498","https://openalex.org/W4289286627","https://openalex.org/W2097408449"],"abstract_inverted_index":{"In":[0],"this":[1,27,34],"paper,":[2],"we":[3,49,67,105,124],"shall":[4,20,50,68,77,106],"study":[5],"the":[6,11,16,23,31,38,43,80,85,91,117,121,134],"parabolic-elliptic":[7],"Keller--Segel":[8],"system":[9],"on":[10,84,133],"Poincar\u00e9":[12],"disk":[13],"model":[14],"of":[15,26,33,120,130],"two-dimensional-hyperbolic":[17],"space.":[18],"We":[19,76],"investigate":[21],"how":[22],"negative":[24],"curvature":[25],"Riemannian":[28],"manifold":[29],"influences":[30],"solutions":[32],"system.":[35],"As":[36],"in":[37,96],"two-dimensional":[39],"Euclidean":[40],"case,":[41],"under":[42,111],"subcritical":[44],"condition":[45],"$\\chi":[46,102],"M<":[47],"8\\pi$,":[48],"prove":[51,69,89],"global":[52],"well-posedness":[53],"results":[54],"with":[55],"any":[56],"initial":[57,135],"$L^1$-data.":[58],"More":[59],"precisely,":[60],"by":[61],"using":[62],"dispersive":[63],"and":[64],"smoothing":[65],"estimates":[66,83],"Fujita--Kato":[70],"type":[71,132],"theorems":[72],"for":[73,137],"local":[74],"well-posedness.":[75],"then":[78],"use":[79],"logarithmic":[81],"Hardy--Littlewood--Sobolev":[82],"hyperbolic":[86,122],"space":[87],"to":[88,116],"that":[90],"solution":[92],"cannot":[93],"blow":[94],"up":[95],"finite":[97],"time.":[98],"For":[99],"larger":[100],"mass":[101],"M>":[103],"8\\pi$":[104],"obtain":[107],"a":[108,126],"blow-up":[109],"result":[110],"an":[112],"additional":[113],"condition.":[114],"According":[115],"exponential":[118,131],"growth":[119],"space,":[123],"find":[125],"suitable":[127],"weighted":[128],"moment":[129],"data":[136],"blow-up.":[138]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
