{"id":"https://openalex.org/W2056202747","doi":"https://doi.org/10.1137/s0036141001385046","title":"Mathematical Analysis of a Model for the Initiation of Angiogenesis","display_name":"Mathematical Analysis of a Model for the Initiation of Angiogenesis","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2056202747","doi":"https://doi.org/10.1137/s0036141001385046","mag":"2056202747"},"language":"en","primary_location":{"id":"doi:10.1137/s0036141001385046","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141001385046","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/A5044177527","display_name":"Marco A. Fontelos","orcid":"https://orcid.org/0000-0003-4986-1752"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Marco A. Fontelos","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027260022","display_name":"Avner Friedman","orcid":"https://orcid.org/0000-0002-7875-174X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Avner Friedman","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5049030931","display_name":"Bei Hu","orcid":"https://orcid.org/0000-0002-1602-845X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bei Hu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5044177527"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.587,"has_fulltext":false,"cited_by_count":137,"citation_normalized_percentile":{"value":0.95995071,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"33","issue":"6","first_page":"1330","last_page":"1355"},"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9825000166893005,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.769454836845398},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.7576191425323486},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6096909642219543},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5861020684242249},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5566697716712952},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4729328453540802},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.47162365913391113},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08652064204216003}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.769454836845398},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.7576191425323486},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6096909642219543},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5861020684242249},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5566697716712952},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4729328453540802},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.47162365913391113},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08652064204216003},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036141001385046","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141001385046","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:10.1.1.585.8652","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.585.8652","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.escet.urjc.es/~mafontel/angio.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Partnerships for the goals","id":"https://metadata.un.org/sdg/17","score":0.4399999976158142}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W13443198","https://openalex.org/W1841343875","https://openalex.org/W1973692656","https://openalex.org/W1980812171","https://openalex.org/W1981659355","https://openalex.org/W1997585819","https://openalex.org/W2000370113","https://openalex.org/W2006798765","https://openalex.org/W2011804741","https://openalex.org/W2021117151","https://openalex.org/W2024950441","https://openalex.org/W2042892258","https://openalex.org/W2048195900","https://openalex.org/W2060402190","https://openalex.org/W2089692468","https://openalex.org/W4246744041"],"related_works":["https://openalex.org/W2960434112","https://openalex.org/W3049714198","https://openalex.org/W2036805113","https://openalex.org/W2592279130","https://openalex.org/W2048010006","https://openalex.org/W2118964038","https://openalex.org/W2999616507","https://openalex.org/W3164276969","https://openalex.org/W2029287765","https://openalex.org/W2043671984"],"abstract_inverted_index":{"In":[0,65],"this":[1],"paper":[2],"we":[3,67],"consider":[4],"a":[5,28,33,52],"nonlinear":[6],"system":[7,25,50],"of":[8,13,31,35,37],"partial":[9],"differential":[10,20],"equations":[11,21],"consisting":[12],"one":[14],"parabolic":[15],"equation":[16],"and":[17,56],"two":[18],"ordinary":[19],"in":[22,27],"t.":[23],"The":[24],"arises":[26],"mathematical":[29],"model":[30],"angiogenesis,":[32],"process":[34],"sprouting":[36],"new":[38],"blood":[39],"vessels":[40],"from":[41],"an":[42],"existing":[43],"vascular":[44],"network.":[45],"We":[46],"prove":[47],"that":[48,69],"the":[49],"has":[51],"unique":[53],"global":[54],"solution":[55],"study":[57],"its":[58],"asymptotic":[59],"behavior":[60],"as":[61],"$t\\rightarrow":[62],"\\infty":[63],"$.":[64],"particular,":[66],"show":[68],"stationary":[70],"solutions":[71],"are":[72],"local":[73],"attractors.":[74]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":12},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":16},{"year":2019,"cited_by_count":15},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":9}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}