{"id":"https://openalex.org/W2808437636","doi":"https://doi.org/10.1137/17m1144647","title":"Boundedness, Stabilization, and Pattern Formation Driven by Density-Suppressed Motility","display_name":"Boundedness, Stabilization, and Pattern Formation Driven by Density-Suppressed Motility","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2808437636","doi":"https://doi.org/10.1137/17m1144647","mag":"2808437636"},"language":"en","primary_location":{"id":"doi:10.1137/17m1144647","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1144647","pdf_url":null,"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":null,"license_id":null,"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":"green","oa_url":"http://ira.lib.polyu.edu.hk/bitstream/10397/95576/1/17m1144647.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102838622","display_name":"Hai\u2010Yang Jin","orcid":null},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hai-Yang Jin","raw_affiliation_strings":["Department of Mathematics, South China University of Technology, Guangzhou 510640, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, South China University of Technology, Guangzhou 510640, China","institution_ids":["https://openalex.org/I90610280"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058009844","display_name":"Yong-Jung Kim","orcid":"https://orcid.org/0000-0003-0968-4093"},"institutions":[{"id":"https://openalex.org/I157485424","display_name":"Korea Advanced Institute of Science and Technology","ror":"https://ror.org/05apxxy63","country_code":"KR","type":"education","lineage":["https://openalex.org/I157485424"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Yong-Jung Kim","raw_affiliation_strings":["Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon, 34141, Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon, 34141, Korea","institution_ids":["https://openalex.org/I157485424"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031464759","display_name":"Zhi\u2010An Wang","orcid":"https://orcid.org/0000-0003-2945-5810"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Zhi-An Wang","raw_affiliation_strings":["Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Hong Kong","institution_ids":["https://openalex.org/I14243506"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5102838622"],"corresponding_institution_ids":["https://openalex.org/I90610280"],"apc_list":null,"apc_paid":null,"fwci":7.4192,"has_fulltext":true,"cited_by_count":188,"citation_normalized_percentile":{"value":0.97934386,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"78","issue":"3","first_page":"1632","last_page":"1657"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":1.0,"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":1.0,"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/T13362","display_name":"Slime Mold and Myxomycetes Research","score":0.9930999875068665,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9912999868392944,"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/bounded-function","display_name":"Bounded function","score":0.5206438899040222},{"id":"https://openalex.org/keywords/degeneracy","display_name":"Degeneracy (biology)","score":0.4817888140678406},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4707643985748291},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4519183933734894},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4491720199584961},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34572088718414307},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3046823740005493}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5206438899040222},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.4817888140678406},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4707643985748291},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4519183933734894},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4491720199584961},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34572088718414307},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3046823740005493},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/17m1144647","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1144647","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/95576","is_oa":true,"landing_page_url":"http://hdl.handle.net/10397/95576","pdf_url":"http://ira.lib.polyu.edu.hk/bitstream/10397/95576/1/17m1144647.pdf","source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal/Magazine Article"},{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/78559","is_oa":false,"landing_page_url":"http://hdl.handle.net/10397/78559","pdf_url":null,"source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal/Magazine Article"}],"best_oa_location":{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/95576","is_oa":true,"landing_page_url":"http://hdl.handle.net/10397/95576","pdf_url":"http://ira.lib.polyu.edu.hk/bitstream/10397/95576/1/17m1144647.pdf","source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal/Magazine Article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1174443052","display_name":null,"funder_award_id":"11501218","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3389021101","display_name":null,"funder_award_id":"2017MS107","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G503080312","display_name":null,"funder_award_id":"PolyU 153041/15P","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G5999429524","display_name":null,"funder_award_id":"PolyU 153032/15P","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321592","display_name":"Research Grants Council, University Grants Committee","ror":"https://ror.org/00djwmt25"},{"id":"https://openalex.org/F4320322598","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2808437636.pdf","grobid_xml":"https://content.openalex.org/works/W2808437636.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W1969861965","https://openalex.org/W1975961081","https://openalex.org/W1990021158","https://openalex.org/W1991933227","https://openalex.org/W2011513906","https://openalex.org/W2021117151","https://openalex.org/W2023884962","https://openalex.org/W2037486322","https://openalex.org/W2039039511","https://openalex.org/W2046495918","https://openalex.org/W2046565293","https://openalex.org/W2049223241","https://openalex.org/W2054870756","https://openalex.org/W2061439938","https://openalex.org/W2073145883","https://openalex.org/W2077209084","https://openalex.org/W2078929283","https://openalex.org/W2081542877","https://openalex.org/W2089510219","https://openalex.org/W2093633760","https://openalex.org/W2097085483","https://openalex.org/W2109177343","https://openalex.org/W2111173827","https://openalex.org/W2138711501","https://openalex.org/W2142491793","https://openalex.org/W2168152765","https://openalex.org/W2345757597","https://openalex.org/W2393531932","https://openalex.org/W2534946191","https://openalex.org/W2564287736","https://openalex.org/W2620153755","https://openalex.org/W2963970869","https://openalex.org/W2964209903"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2372940580","https://openalex.org/W2101113459","https://openalex.org/W2187706389","https://openalex.org/W4401569525","https://openalex.org/W1970824047","https://openalex.org/W1941883603","https://openalex.org/W4207069403","https://openalex.org/W2964287305","https://openalex.org/W4220826729"],"abstract_inverted_index":{"We":[0],"are":[1],"concerned":[2],"with":[3,23,138,147],"the":[4,29,73,81,87,97,107,115,124,128,135,152,184],"following":[5],"density-suppressed":[6,59,77],"motility":[7,30,60,78,98],"model:":[8],"$u_t=\\Delta":[9],"(\\gamma(v)":[10],"u)+\\mu":[11],"u(1-u);":[12],"v_t=\\Delta":[13],"v+":[14],"u-v,$":[15],"in":[16,72],"a":[17,55,102,116,139],"bounded":[18],"smooth":[19],"domain":[20],"$\\Omega\\subset":[21],"\\mathbb{R}^2$":[22],"homogeneous":[24],"Neumann":[25],"boundary":[26],"conditions,":[27],"where":[28],"function":[31,99,104],"$\\gamma(v)\\in":[32],"C^3([0,\\infty))$,":[33],"$\\gamma":[34],"(v)>0$,":[35],"$\\gamma'(v)<0$":[36],"for":[37],"all":[38],"$v\\geq":[39],"0$,":[40],"$\\lim_{v":[41,45,89],"\\to":[42,46,90],"\\infty}\\gamma(v)=0$,":[43],"and":[44,105,126,179],"\\infty}\\frac{\\gamma'(v)}{\\gamma(v)}$":[47],"exists.":[48],"The":[49,68],"model":[50,79],"is":[51,80,157],"proposed":[52],"to":[53,121,175],"advocate":[54],"new":[56],"possible":[57,82],"mechanism:":[58],"can":[61],"induce":[62],"spatio-temporal":[63],"pattern":[64,163],"formation":[65,164],"through":[66],"self-trapping.":[67],"major":[69],"technical":[70],"difficulty":[71],"analysis":[74],"of":[75,84,109,119,131,134],"above":[76,136],"degeneracy":[83,125],"diffusion":[85],"from":[86],"condition":[88],"\\infty}\\gamma(v)=0$.":[91],"In":[92],"this":[93],"paper,":[94],"by":[95,183],"treating":[96],"$\\gamma(v)$":[100],"as":[101],"weight":[103],"employing":[106],"method":[108],"weighted":[110],"energy":[111],"estimates,":[112],"we":[113,143,171],"derive":[114],"priori":[117],"$L^\\infty$-bound":[118],"$v$":[120],"rule":[122],"out":[123],"establish":[127],"global":[129],"existence":[130],"classical":[132],"solutions":[133],"problem":[137],"uniform-in-time":[140],"bound.":[141],"Furthermore,":[142],"show":[144],"if":[145],"$\\mu>\\frac{K_0}{16}$":[146],"$K_0=\\max_{0\\leq":[148],"v":[149],"\\leq":[150],"\\infty}\\frac{|\\gamma'(v)|^2}{\\gamma(v)}$,":[151],"constant":[153],"steady":[154],"state":[155],"(1,1)":[156],"globally":[158],"asymptotically":[159],"stable":[160],"and,":[161],"hence,":[162],"does":[165],"not":[166],"exist.":[167],"For":[168],"small":[169],"$\\mu>0$,":[170],"perform":[172],"numerical":[173],"simulations":[174],"illustrate":[176],"aggregation":[177],"patterns":[178],"wave":[180],"propagation":[181],"formed":[182],"model.":[185]},"counts_by_year":[{"year":2026,"cited_by_count":8},{"year":2025,"cited_by_count":40},{"year":2024,"cited_by_count":33},{"year":2023,"cited_by_count":22},{"year":2022,"cited_by_count":30},{"year":2021,"cited_by_count":21},{"year":2020,"cited_by_count":25},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":1}],"updated_date":"2026-05-04T08:30:34.212998","created_date":"2025-10-10T00:00:00"}
