{"id":"https://openalex.org/W2005141382","doi":"https://doi.org/10.1137/s0036141003427798","title":"Analysis of a Multidimensional Parabolic Population Model with Strong Cross-Diffusion","display_name":"Analysis of a Multidimensional Parabolic Population Model with Strong Cross-Diffusion","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2005141382","doi":"https://doi.org/10.1137/s0036141003427798","mag":"2005141382"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141003427798","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_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5039809829","display_name":"Li Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"funder","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li Chen","raw_affiliation_strings":["Tsinghua University"],"affiliations":[{"raw_affiliation_string":"Tsinghua University","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084423759","display_name":"Ansgar J\u00fcngel","orcid":"https://orcid.org/0000-0003-0633-8929"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ansgar J\u00fcngel","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.026,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":148,"citation_normalized_percentile":{"value":0.977755,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"36","issue":"1","first_page":"301","last_page":"322"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9998,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9998,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9985,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9834,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/population-model","display_name":"Population model","score":0.44339025},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.44029254}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.89212954},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.63253313},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.55807817},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.47741115},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47450444},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.4472724},{"id":"https://openalex.org/C52079815","wikidata":"https://www.wikidata.org/wiki/Q7229808","display_name":"Population model","level":3,"score":0.44339025},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.44029254},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40363482},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.071467996},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141003427798","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_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.46}],"grants":[],"datasets":[],"versions":[],"referenced_works_count":25,"referenced_works":["https://openalex.org/W1969385392","https://openalex.org/W1972710903","https://openalex.org/W1973118029","https://openalex.org/W1976752429","https://openalex.org/W1979599605","https://openalex.org/W1992831515","https://openalex.org/W2003018740","https://openalex.org/W2011660839","https://openalex.org/W2014205890","https://openalex.org/W2020482432","https://openalex.org/W2022088322","https://openalex.org/W2026570637","https://openalex.org/W2028568954","https://openalex.org/W2033518856","https://openalex.org/W2041142520","https://openalex.org/W2049886781","https://openalex.org/W2060684813","https://openalex.org/W2061245907","https://openalex.org/W2066496593","https://openalex.org/W2073078790","https://openalex.org/W2077313431","https://openalex.org/W2081225921","https://openalex.org/W22533412","https://openalex.org/W236298470","https://openalex.org/W3145909966"],"related_works":["https://openalex.org/W4313705710","https://openalex.org/W4226067901","https://openalex.org/W3157737782","https://openalex.org/W3117324600","https://openalex.org/W3043663456","https://openalex.org/W2910133962","https://openalex.org/W2401850100","https://openalex.org/W2141704600","https://openalex.org/W2020174565","https://openalex.org/W2015671406"],"abstract_inverted_index":{"The":[0,21,53],"global":[1],"existence":[2,57],"of":[3,24,55,63,73],"a":[4,9,60,78],"nonnegative":[5],"weak":[6],"solution":[7],"to":[8,50],"multidimensional":[10],"parabolic":[11],"strongly":[12],"coupled":[13],"model":[14,26],"for":[15],"two":[16],"competing":[17],"species":[18],"is":[19,27,32],"proved.":[20],"main":[22],"feature":[23],"the":[25,29,41,56,64,71],"that":[28,40],"diffusion":[30],"matrix":[31,43],"nonsymmetric":[33],"and":[34,39,70],"generally":[35],"not":[36],"positive":[37],"definite":[38],"nondiagonal":[42],"elements":[44],"(the":[45],"cross-diffusion":[46,65],"terms)":[47],"are":[48,59],"allowed":[49],"be":[51],"\"large.\"":[52],"ideas":[54],"proof":[58],"careful":[61],"approximation":[62],"terms":[66],"using":[67],"finite":[68],"differences":[69],"use":[72],"an":[74],"entropy":[75],"inequality":[76],"yielding":[77],"priori":[79],"estimates.":[80]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2005141382","counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":18},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":13},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":8}],"updated_date":"2025-03-17T21:26:50.738182","created_date":"2016-06-24"}