{"id":"https://openalex.org/W2094940662","doi":"https://doi.org/10.1137/100783674","title":"Nonlinear Cross-Diffusion with Size Exclusion","display_name":"Nonlinear Cross-Diffusion with Size Exclusion","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2094940662","doi":"https://doi.org/10.1137/100783674","mag":"2094940662"},"language":"en","primary_location":{"id":"doi:10.1137/100783674","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100783674","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/A5069220813","display_name":"Martin Burger","orcid":"https://orcid.org/0000-0003-2619-2912"},"institutions":[{"id":"https://openalex.org/I22465464","display_name":"University of M\u00fcnster","ror":"https://ror.org/00pd74e08","country_code":"DE","type":"education","lineage":["https://openalex.org/I22465464"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Burger","raw_affiliation_strings":["#N##TAB##TAB##TAB##TAB# University of M\u00fcnster#N##TAB##TAB##TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"#N##TAB##TAB##TAB##TAB# University of M\u00fcnster#N##TAB##TAB##TAB#","institution_ids":["https://openalex.org/I22465464"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057909382","display_name":"Marco Di Francesco","orcid":"https://orcid.org/0000-0001-5412-8315"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marco Di Francesco","raw_affiliation_strings":["Department of Mathematical Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029122330","display_name":"Jan\u2010Frederik Pietschmann","orcid":"https://orcid.org/0000-0003-0383-8696"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jan-Frederik Pietschmann","raw_affiliation_strings":["University of Cambridge,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Cambridge,","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028559352","display_name":"B\u00e4rbel Schlake","orcid":null},"institutions":[{"id":"https://openalex.org/I22465464","display_name":"University of M\u00fcnster","ror":"https://ror.org/00pd74e08","country_code":"DE","type":"education","lineage":["https://openalex.org/I22465464"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"B\u00e4rbel Schlake","raw_affiliation_strings":["#N##TAB##TAB##TAB##TAB# University of M\u00fcnster#N##TAB##TAB##TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"#N##TAB##TAB##TAB##TAB# University of M\u00fcnster#N##TAB##TAB##TAB#","institution_ids":["https://openalex.org/I22465464"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7777,"has_fulltext":false,"cited_by_count":114,"citation_normalized_percentile":{"value":0.89301035,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"42","issue":"6","first_page":"2842","last_page":"2871"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9998000264167786,"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":0.9998000264167786,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.995199978351593,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7803125381469727},{"id":"https://openalex.org/keywords/degeneracy","display_name":"Degeneracy (biology)","score":0.7457209229469299},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7252354621887207},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.6651412844657898},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5202804207801819},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4032258093357086},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3967159688472748},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10365474224090576},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.058514297008514404}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7803125381469727},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.7457209229469299},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7252354621887207},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.6651412844657898},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5202804207801819},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4032258093357086},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3967159688472748},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10365474224090576},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.058514297008514404},{"id":"https://openalex.org/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/100783674","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100783674","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:10.1.1.394.5902","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.394.5902","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://wwwmath.uni-muenster.de/u/schlake/78367.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.642.6147","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.642.6147","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://wwwmath.uni-muenster.de/num/publications/2010/BDPS10/WithoutPotential.pdf","raw_type":"text"},{"id":"pmh:oai:repository.kaust.edu.sa:10754/598987","is_oa":false,"landing_page_url":"http://hdl.handle.net/10754/598987","pdf_url":null,"source":{"id":"https://openalex.org/S4306401596","display_name":"King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71920554","host_organization_name":"King Abdullah University of Science and Technology","host_organization_lineage":["https://openalex.org/I71920554"],"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"},{"id":"pmh:oai:uni-augsburg.opus-bayern.de:101989","is_oa":false,"landing_page_url":"https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/101989","pdf_url":null,"source":{"id":"https://openalex.org/S4306400930","display_name":"OPUS (Augsburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119916105","host_organization_name":"Augsburg University","host_organization_lineage":["https://openalex.org/I119916105"],"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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land","score":0.6000000238418579}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1217515891","https://openalex.org/W1534983138","https://openalex.org/W1544168072","https://openalex.org/W1995258771","https://openalex.org/W1996552378","https://openalex.org/W2000370113","https://openalex.org/W2001222525","https://openalex.org/W2005141382","https://openalex.org/W2006369296","https://openalex.org/W2008920240","https://openalex.org/W2011135195","https://openalex.org/W2012405657","https://openalex.org/W2031088533","https://openalex.org/W2033468335","https://openalex.org/W2042892258","https://openalex.org/W2054723044","https://openalex.org/W2064389898","https://openalex.org/W2071048859","https://openalex.org/W2074203477","https://openalex.org/W2077070574","https://openalex.org/W2077492329","https://openalex.org/W2078936959","https://openalex.org/W2079516848","https://openalex.org/W2105582005","https://openalex.org/W2110769108","https://openalex.org/W2127674094","https://openalex.org/W2167152334","https://openalex.org/W2369386221","https://openalex.org/W2373444117","https://openalex.org/W3101978293","https://openalex.org/W3121932189","https://openalex.org/W4244836353","https://openalex.org/W4246744041","https://openalex.org/W4249698154"],"related_works":["https://openalex.org/W2372940580","https://openalex.org/W2101113459","https://openalex.org/W2187706389","https://openalex.org/W1970824047","https://openalex.org/W1941883603","https://openalex.org/W1842556415","https://openalex.org/W4252688432","https://openalex.org/W2555734889","https://openalex.org/W1675409203","https://openalex.org/W173474148"],"abstract_inverted_index":{"The":[0,24],"aim":[1],"of":[2,11,17,45,52,57,68,79],"this":[3],"paper":[4],"is":[5],"to":[6,30,61],"investigate":[7],"the":[8,43,46,69,76],"mathematical":[9],"properties":[10],"a":[12],"continuum":[13],"model":[14],"for":[15,26],"diffusion":[16],"multiple":[18],"species":[19,28],"incorporating":[20],"size":[21],"exclusion":[22],"effects.":[23],"system":[25],"two":[27],"leads":[29],"nonlinear":[31],"cross-diffusion":[32],"terms":[33],"with":[34],"double":[35],"degeneracy,":[36],"which":[37],"creates":[38],"significant":[39],"novel":[40],"challenges":[41],"in":[42,72],"analysis":[44],"system.":[47],"We":[48,63],"prove":[49],"global":[50],"existence":[51],"weak":[53],"solutions":[54,59],"and":[55,71],"well-posedness":[56],"strong":[58],"close":[60],"equilibrium.":[62],"further":[64],"study":[65],"some":[66],"asymptotics":[67],"model,":[70],"particular":[73],"we":[74],"characterize":[75],"large-time":[77],"behavior":[78],"solutions.":[80]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":12},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
