{"id":"https://openalex.org/W2012651190","doi":"https://doi.org/10.1137/130922100","title":"Asymptotic Behavior of a Nonlocal Diffusive Logistic Equation","display_name":"Asymptotic Behavior of a Nonlocal Diffusive Logistic Equation","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2012651190","doi":"https://doi.org/10.1137/130922100","mag":"2012651190"},"language":"en","primary_location":{"id":"doi:10.1137/130922100","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130922100","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/A5111055166","display_name":"Arnaud Ducrot","orcid":null},"institutions":[{"id":"https://openalex.org/I4210166017","display_name":"Institut de Math\u00e9matiques de Bordeaux","ror":"https://ror.org/05m3r1b84","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I15057530","https://openalex.org/I4210141950","https://openalex.org/I4210160189","https://openalex.org/I4210166017"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Arnaud Ducrot","raw_affiliation_strings":["Institut de Math\u00e9matiques de Bordeaux"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Bordeaux","institution_ids":["https://openalex.org/I4210166017"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035929676","display_name":"Pierre Magal","orcid":"https://orcid.org/0000-0002-4776-0061"},"institutions":[{"id":"https://openalex.org/I4210166017","display_name":"Institut de Math\u00e9matiques de Bordeaux","ror":"https://ror.org/05m3r1b84","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I15057530","https://openalex.org/I4210141950","https://openalex.org/I4210160189","https://openalex.org/I4210166017"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pierre Magal","raw_affiliation_strings":["Institut de Math\u00e9matiques de Bordeaux"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Bordeaux","institution_ids":["https://openalex.org/I4210166017"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210166017"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.08053815,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"46","issue":"3","first_page":"1731","last_page":"1753"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9995999932289124,"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":0.9995999932289124,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/mathematics","display_name":"Mathematics","score":0.7909226417541504},{"id":"https://openalex.org/keywords/logistic-function","display_name":"Logistic function","score":0.6758913993835449},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.6432480812072754},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.5793413519859314},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5654159188270569},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.5286415219306946},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.45855802297592163},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4195822477340698},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4016449451446533},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15571483969688416},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.13139450550079346},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12954741716384888},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07261830568313599},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06788861751556396}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7909226417541504},{"id":"https://openalex.org/C180802074","wikidata":"https://www.wikidata.org/wiki/Q1052379","display_name":"Logistic function","level":2,"score":0.6758913993835449},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.6432480812072754},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.5793413519859314},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5654159188270569},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.5286415219306946},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.45855802297592163},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4195822477340698},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4016449451446533},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15571483969688416},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.13139450550079346},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12954741716384888},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07261830568313599},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06788861751556396},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"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":5,"locations":[{"id":"doi:10.1137/130922100","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130922100","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:CiteSeerX.psu:10.1.1.714.1488","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.714.1488","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.u-bordeaux1.fr/%7Epmagal100p/papers/DM-SIAM%20JMA14.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00993008v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00993008","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Mathematical Analysis, 2014, 46 (3), pp.1731-1753. ⟨10.1137/130922100⟩","raw_type":"Journal articles"},{"id":"pmh:oai:oskar-bordeaux.fr:20.500.12278/114638","is_oa":false,"landing_page_url":"https://oskar-bordeaux.fr/handle/20.500.12278/114638","pdf_url":null,"source":{"id":"https://openalex.org/S4306402569","display_name":"Oskar-Bordeaux (Universite de Bordeaux)","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article de revue"},{"id":"pmh:oai:oskar-bordeaux.fr:20.500.12278/189255","is_oa":false,"landing_page_url":"https://oskar-bordeaux.fr/handle/20.500.12278/189255","pdf_url":null,"source":{"id":"https://openalex.org/S4306402569","display_name":"Oskar-Bordeaux (Universite de Bordeaux)","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article de revue"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.8299999833106995,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W27423464","https://openalex.org/W1509925099","https://openalex.org/W1516255585","https://openalex.org/W1551516234","https://openalex.org/W1597623287","https://openalex.org/W1963810041","https://openalex.org/W1987588325","https://openalex.org/W1990966336","https://openalex.org/W2003297161","https://openalex.org/W2006078471","https://openalex.org/W2017992740","https://openalex.org/W2031055103","https://openalex.org/W2032643447","https://openalex.org/W2044447043","https://openalex.org/W2048351666","https://openalex.org/W2073063542","https://openalex.org/W2081207514","https://openalex.org/W2111914545","https://openalex.org/W2120730878","https://openalex.org/W2126564632","https://openalex.org/W2155385278","https://openalex.org/W2156934943","https://openalex.org/W2161765142","https://openalex.org/W2165485564","https://openalex.org/W2171306535","https://openalex.org/W2802739963","https://openalex.org/W3103533148","https://openalex.org/W3104332327"],"related_works":["https://openalex.org/W2121543990","https://openalex.org/W2402800040","https://openalex.org/W2000020320","https://openalex.org/W4252969132","https://openalex.org/W1981078319","https://openalex.org/W2008917324","https://openalex.org/W2581541046","https://openalex.org/W4387315838","https://openalex.org/W2805799113","https://openalex.org/W2077709279"],"abstract_inverted_index":{"The":[0,15,68],"long":[1,65],"time":[2,66],"behavior":[3],"of":[4,11,37,56,70,73,81],"a":[5,27,34,40],"logistic-type":[6],"equation":[7,16],"modeling":[8],"the":[9,48,54,57,74,82,92,96],"motion":[10,36],"cells":[12,38],"is":[13,76],"investigated.":[14],"we":[17,51],"consider":[18],"takes":[19],"into":[20],"account":[21],"birth":[22],"and":[23],"death":[24],"processes":[25],"using":[26,39],"simple":[28],"logistic":[29],"effect":[30],"as":[31,33],"well":[32],"nonlocal":[35,41],"Darcy's":[42],"law":[43],"with":[44],"regular":[45],"kernel.":[46],"Using":[47],"periodic":[49],"framework":[50],"first":[52],"investigate":[53],"well-posedness":[55],"problem":[58],"before":[59],"deriving":[60],"some":[61],"information":[62],"about":[63],"its":[64],"behavior.":[67],"lack":[69],"asymptotic":[71],"compactness":[72],"system":[75],"overcome":[77],"by":[78],"making":[79],"use":[80],"Young":[83,97],"measure":[84,98],"theory.":[85],"This":[86],"allows":[87],"us":[88],"to":[89],"conclude":[90],"that":[91],"semiflow":[93],"converges":[94],"for":[95],"topology.":[99]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}