{"id":"https://openalex.org/W2612414054","doi":"https://doi.org/10.1137/17m1128782","title":"Zoology of a Nonlocal Cross-Diffusion Model for Two Species","display_name":"Zoology of a Nonlocal Cross-Diffusion Model for Two Species","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2612414054","doi":"https://doi.org/10.1137/17m1128782","mag":"2612414054"},"language":"en","primary_location":{"id":"doi:10.1137/17m1128782","is_oa":true,"landing_page_url":"https://doi.org/10.1137/17m1128782","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/17M1128782","source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/17M1128782","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022412709","display_name":"Jos\u00e9 A. Carrillo","orcid":"https://orcid.org/0000-0001-8819-4660"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Jos\u00e9 A. Carrillo","raw_affiliation_strings":["Department of Mathematics, Imperial College London, SW7 2AZ London, UK"],"raw_orcid":"https://orcid.org/0000-0001-8819-4660","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Imperial College London, SW7 2AZ London, UK","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072428176","display_name":"Yanghong Huang","orcid":"https://orcid.org/0000-0003-4145-6621"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Yanghong Huang","raw_affiliation_strings":["School of Mathematics, The University of Manchester, Manchester M13 9PL, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, The University of Manchester, Manchester M13 9PL, UK","institution_ids":["https://openalex.org/I28407311"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044472816","display_name":"Markus Schmidtchen","orcid":"https://orcid.org/0000-0001-9662-3111"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Markus Schmidtchen","raw_affiliation_strings":["Department of Mathematics, Imperial College London, SW7 2AZ London, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Imperial College London, SW7 2AZ London, UK","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5022412709"],"corresponding_institution_ids":["https://openalex.org/I47508984"],"apc_list":null,"apc_paid":null,"fwci":7.1826,"has_fulltext":false,"cited_by_count":86,"citation_normalized_percentile":{"value":0.97188392,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"78","issue":"2","first_page":"1078","last_page":"1104"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9987999796867371,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.6604645848274231},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5612727999687195},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.537908136844635},{"id":"https://openalex.org/keywords/thermal-diffusivity","display_name":"Thermal diffusivity","score":0.45529770851135254},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.4302583932876587},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32264602184295654},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.165390282869339}],"concepts":[{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6604645848274231},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5612727999687195},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.537908136844635},{"id":"https://openalex.org/C37668627","wikidata":"https://www.wikidata.org/wiki/Q3381809","display_name":"Thermal diffusivity","level":2,"score":0.45529770851135254},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.4302583932876587},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32264602184295654},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.165390282869339}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/17m1128782","is_oa":true,"landing_page_url":"https://doi.org/10.1137/17m1128782","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/17M1128782","source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:70a7af72-716d-4fda-9bc9-14c348a40619","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:70a7af72-716d-4fda-9bc9-14c348a40619","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements","raw_type":"Journal article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/67ca6dec-f555-40af-b2f9-ff23c86804fd","is_oa":true,"landing_page_url":"https://research.manchester.ac.uk/en/publications/67ca6dec-f555-40af-b2f9-ff23c86804fd","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Carrillo, J A, Huang, Y & Schmidtchen, M 2018, 'Zoology of a non-local cross-diffusion model for two species', SIAM JOURNAL ON APPLIED MATHEMATICS, vol. 78, no. 2, pp. 1078-1104. https://doi.org/10.1137/17M1128782","raw_type":"article"},{"id":"pmh:oai:pure.atira.dk:publications/67ca6dec-f555-40af-b2f9-ff23c86804fd","is_oa":true,"landing_page_url":"https://www.research.manchester.ac.uk/portal/en/publications/zoology-of-a-nonlocal-crossdiffusion-model-for-two-species(67ca6dec-f555-40af-b2f9-ff23c86804fd).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Carrillo, J A, Huang, Y & Schmidtchen, M 2018, 'Zoology of a non-local cross-diffusion model for two species', SIAM JOURNAL ON APPLIED MATHEMATICS, vol. 78, no. 2, pp. 1078-1104. https://doi.org/10.1137/17M1128782","raw_type":"article"},{"id":"pmh:oai:spiral.imperial.ac.uk:10044/1/56580","is_oa":true,"landing_page_url":"http://hdl.handle.net/10044/1/56580","pdf_url":null,"source":{"id":"https://openalex.org/S4306401396","display_name":"Spiral (Imperial College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I47508984","host_organization_name":"Imperial College London","host_organization_lineage":["https://openalex.org/I47508984"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"1104","raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.1137/17m1128782","is_oa":true,"landing_page_url":"https://doi.org/10.1137/17m1128782","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/17M1128782","source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7300000190734863,"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land"}],"awards":[{"id":"https://openalex.org/G1257954173","display_name":null,"funder_award_id":"EP/P031587/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4787172370","display_name":"Nonlocal Partial Differential Equations: entropies, gradient flows, phase transitions and applications","funder_award_id":"EP/P031587/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320320006","display_name":"Royal Society","ror":"https://ror.org/03wnrjx87"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W256659003","https://openalex.org/W1482888786","https://openalex.org/W1605032588","https://openalex.org/W1963640358","https://openalex.org/W1973118029","https://openalex.org/W1975529482","https://openalex.org/W1985718502","https://openalex.org/W1987588325","https://openalex.org/W1999083427","https://openalex.org/W2020995965","https://openalex.org/W2024948945","https://openalex.org/W2027077768","https://openalex.org/W2032168148","https://openalex.org/W2042564923","https://openalex.org/W2045783965","https://openalex.org/W2051601201","https://openalex.org/W2054821686","https://openalex.org/W2058747001","https://openalex.org/W2059430409","https://openalex.org/W2061245907","https://openalex.org/W2067258650","https://openalex.org/W2071048859","https://openalex.org/W2072076940","https://openalex.org/W2072921143","https://openalex.org/W2077289604","https://openalex.org/W2087873587","https://openalex.org/W2098870063","https://openalex.org/W2103714988","https://openalex.org/W2116463680","https://openalex.org/W2119323323","https://openalex.org/W2119414533","https://openalex.org/W2130062345","https://openalex.org/W2151793824","https://openalex.org/W2155385278","https://openalex.org/W2156934943","https://openalex.org/W2157942701","https://openalex.org/W2165908886","https://openalex.org/W2168688381","https://openalex.org/W2190106403","https://openalex.org/W2327285036","https://openalex.org/W2563137475","https://openalex.org/W2962785408","https://openalex.org/W3100014801","https://openalex.org/W4255612286"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2385382668","https://openalex.org/W2283102826","https://openalex.org/W1974236007","https://openalex.org/W2023596821","https://openalex.org/W2351460627","https://openalex.org/W2100701926","https://openalex.org/W2335514579","https://openalex.org/W2079698632","https://openalex.org/W2188581046"],"abstract_inverted_index":{"We":[0,10,75,122],"study":[1],"a":[2,12,66,87,124],"nonlocal":[3],"two":[4],"species":[5],"cross-interaction":[6],"model":[7,44,68],"with":[8,109],"cross-diffusion.":[9],"propose":[11],"positivity":[13],"preserving":[14],"finite":[15],"volume":[16],"scheme":[17],"based":[18],"on":[19],"the":[20,53,70,79,82,99,114,119,128,131],"numerical":[21],"method":[22],"introduced":[23],"in":[24,46,69,118,136],"[J.":[25],"A.":[26,28],"Carrillo,":[27],"Chertock,":[29],"and":[30,40,61,96,130],"Y.":[31],"Huang,":[32],"Commun.":[33],"Comput.":[34],"Phys.,":[35],"17":[36],"(2015),":[37],"pp.":[38],"233--258]":[39],"explore":[41],"this":[42],"new":[43],"numerically":[45,129],"terms":[47],"of":[48,72,81,113],"its":[49],"long-time":[50],"behaviors.":[51],"Using":[52],"so-gained":[54],"insights,":[55],"we":[56,97],"compute":[57,98],"analytical":[58],"stationary":[59,107],"states":[60,108,135],"travelling":[62],"pulse":[63],"solutions":[64,91],"for":[65,102,147],"particular":[67,138],"case":[71],"attractive-attractive/attractive-repulsive":[73],"cross-interactions.":[74,104],"show":[76],"that,":[77],"as":[78],"strength":[80],"cross-diffusivity":[83],"decreases,":[84],"there":[85],"is":[86],"transition":[88],"from":[89],"adjacent":[90],"to":[92],"completely":[93],"segregated":[94],"densities,":[95],"threshold":[100],"analytically":[101,132],"attractive-repulsive":[103],"Other":[105],"bifurcating":[106],"various":[110],"coexistence":[111],"components":[112],"support":[115],"are":[116,144],"analyzed":[117],"attractive-attractive":[120],"case.":[121],"find":[123],"strong":[125],"agreement":[126],"between":[127],"computed":[133],"steady":[134],"these":[137],"cases,":[139],"whose":[140],"main":[141],"qualitative":[142],"features":[143],"also":[145],"present":[146],"more":[148],"general":[149],"potentials.":[150]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":13},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":7}],"updated_date":"2026-05-20T08:49:12.498775","created_date":"2025-10-10T00:00:00"}