{"id":"https://openalex.org/W2022010980","doi":"https://doi.org/10.1016/s0096-3003(02)00732-4","title":"Coexistence solutions for a reaction\u2013diffusion system of un-stirred chemostat model","display_name":"Coexistence solutions for a reaction\u2013diffusion system of un-stirred chemostat model","publication_year":2003,"publication_date":"2003-05-12","ids":{"openalex":"https://openalex.org/W2022010980","doi":"https://doi.org/10.1016/s0096-3003(02)00732-4","mag":"2022010980"},"language":"en","primary_location":{"id":"doi:10.1016/s0096-3003(02)00732-4","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0096-3003(02)00732-4","pdf_url":null,"source":{"id":"https://openalex.org/S50372074","display_name":"Applied Mathematics and Computation","issn_l":"0096-3003","issn":["0096-3003","1873-5649"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics and Computation","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/A5101807423","display_name":"Sining Zheng","orcid":"https://orcid.org/0000-0002-7836-3413"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Sining Zheng","raw_affiliation_strings":["Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, PR China","Department of Applied Mathematics, Dalian, University of Technology, Dalian 116024, PR China"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, PR China","institution_ids":["https://openalex.org/I27357992"]},{"raw_affiliation_string":"Department of Applied Mathematics, Dalian, University of Technology, Dalian 116024, PR China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103773312","display_name":"Jing Liu","orcid":"https://orcid.org/0000-0001-5617-2678"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jing Liu","raw_affiliation_strings":["Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, PR China","Department of Applied Mathematics, Dalian, University of Technology, Dalian 116024, PR China"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, PR China","institution_ids":["https://openalex.org/I27357992"]},{"raw_affiliation_string":"Department of Applied Mathematics, Dalian, University of Technology, Dalian 116024, PR China","institution_ids":["https://openalex.org/I27357992"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101807423"],"corresponding_institution_ids":["https://openalex.org/I27357992"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.16871687,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"145","issue":"2-3","first_page":"579","last_page":"590"},"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":0.8701000213623047,"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":0.8701000213623047,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.8284000158309937,"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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.7682999968528748,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/chemostat","display_name":"Chemostat","score":0.9206056594848633},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.6928317546844482},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5989258289337158},{"id":"https://openalex.org/keywords/continuous-stirred-tank-reactor","display_name":"Continuous stirred-tank reactor","score":0.5570919513702393},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.4758446216583252},{"id":"https://openalex.org/keywords/biological-system","display_name":"Biological system","score":0.3886098861694336},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.37987250089645386},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3354484438896179},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.3349158763885498},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2101357877254486},{"id":"https://openalex.org/keywords/physical-chemistry","display_name":"Physical chemistry","score":0.18272584676742554},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.17445462942123413},{"id":"https://openalex.org/keywords/bacteria","display_name":"Bacteria","score":0.09092646837234497}],"concepts":[{"id":"https://openalex.org/C125111812","wikidata":"https://www.wikidata.org/wiki/Q902311","display_name":"Chemostat","level":3,"score":0.9206056594848633},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.6928317546844482},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5989258289337158},{"id":"https://openalex.org/C67334161","wikidata":"https://www.wikidata.org/wiki/Q457904","display_name":"Continuous stirred-tank reactor","level":2,"score":0.5570919513702393},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.4758446216583252},{"id":"https://openalex.org/C186060115","wikidata":"https://www.wikidata.org/wiki/Q30336093","display_name":"Biological system","level":1,"score":0.3886098861694336},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.37987250089645386},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3354484438896179},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.3349158763885498},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2101357877254486},{"id":"https://openalex.org/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","level":1,"score":0.18272584676742554},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.17445462942123413},{"id":"https://openalex.org/C523546767","wikidata":"https://www.wikidata.org/wiki/Q10876","display_name":"Bacteria","level":2,"score":0.09092646837234497},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0096-3003(02)00732-4","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0096-3003(02)00732-4","pdf_url":null,"source":{"id":"https://openalex.org/S50372074","display_name":"Applied Mathematics and Computation","issn_l":"0096-3003","issn":["0096-3003","1873-5649"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Zero hunger","id":"https://metadata.un.org/sdg/2","score":0.6600000262260437}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W135777870","https://openalex.org/W1508747425","https://openalex.org/W1528187561","https://openalex.org/W1589874412","https://openalex.org/W2009137233","https://openalex.org/W2020150158","https://openalex.org/W2032505059","https://openalex.org/W2046724040","https://openalex.org/W2053581978","https://openalex.org/W2060524950","https://openalex.org/W2060838256","https://openalex.org/W2096356504","https://openalex.org/W2125914782","https://openalex.org/W2364036002","https://openalex.org/W2797696350","https://openalex.org/W2983706155","https://openalex.org/W4389367219","https://openalex.org/W7033453288"],"related_works":["https://openalex.org/W1608758340","https://openalex.org/W2123404724","https://openalex.org/W1505019344","https://openalex.org/W4237795480","https://openalex.org/W47420346","https://openalex.org/W2143478158","https://openalex.org/W2025026414","https://openalex.org/W2102268782","https://openalex.org/W2099312222","https://openalex.org/W2073089361"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}