{"id":"https://openalex.org/W3026151519","doi":"https://doi.org/10.1137/19m1268987","title":"Dynamics of Time-Periodic Reaction-Diffusion Equations with Front-Like Initial Data on $\\mathbb{R}$","display_name":"Dynamics of Time-Periodic Reaction-Diffusion Equations with Front-Like Initial Data on $\\mathbb{R}$","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3026151519","doi":"https://doi.org/10.1137/19m1268987","mag":"3026151519"},"language":"en","primary_location":{"id":"doi:10.1137/19m1268987","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1268987","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/A5101451180","display_name":"Weiwei Ding","orcid":"https://orcid.org/0000-0002-5795-8987"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Weiwei Ding","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5037607534","display_name":"Hiroshi Matano","orcid":"https://orcid.org/0000-0002-9944-4677"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hiroshi Matano","raw_affiliation_strings":["\u7814\u7a76\u30fb\u77e5\u8ca1\u6226\u7565\u6a5f\u69cb"],"affiliations":[{"raw_affiliation_string":"\u7814\u7a76\u30fb\u77e5\u8ca1\u6226\u7565\u6a5f\u69cb","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101451180"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.084,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.7933681,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"52","issue":"3","first_page":"2411","last_page":"2462"},"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":0.9991999864578247,"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":0.9991999864578247,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9904000163078308,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9904000163078308,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/heaviside-step-function","display_name":"Heaviside step function","score":0.8052303194999695},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7285686135292053},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7245646715164185},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.5817704796791077},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5569086670875549},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5227009057998657},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4985160827636719},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4499751031398773},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.43967944383621216},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40636909008026123},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3620728850364685},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1776483654975891}],"concepts":[{"id":"https://openalex.org/C7980502","wikidata":"https://www.wikidata.org/wiki/Q322339","display_name":"Heaviside step function","level":2,"score":0.8052303194999695},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7285686135292053},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7245646715164185},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.5817704796791077},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5569086670875549},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5227009057998657},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4985160827636719},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4499751031398773},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.43967944383621216},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40636909008026123},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3620728850364685},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1776483654975891},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1268987","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1268987","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1175671688","display_name":null,"funder_award_id":"16H02151","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G5320015342","display_name":null,"funder_award_id":"17F17021","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W186599579","https://openalex.org/W1545077049","https://openalex.org/W1547920157","https://openalex.org/W1690554132","https://openalex.org/W1693068537","https://openalex.org/W1970915722","https://openalex.org/W2002055895","https://openalex.org/W2012089403","https://openalex.org/W2014863630","https://openalex.org/W2020718248","https://openalex.org/W2034790369","https://openalex.org/W2051791859","https://openalex.org/W2072553848","https://openalex.org/W2075182728","https://openalex.org/W2080127444","https://openalex.org/W2109860009","https://openalex.org/W2123954286","https://openalex.org/W2132099746","https://openalex.org/W2233757937","https://openalex.org/W2342639666","https://openalex.org/W2760284463","https://openalex.org/W2962765913","https://openalex.org/W2962935492","https://openalex.org/W2964253786","https://openalex.org/W2973177480"],"related_works":["https://openalex.org/W2074084660","https://openalex.org/W2901390526","https://openalex.org/W2021508077","https://openalex.org/W2088409529","https://openalex.org/W2077007836","https://openalex.org/W2018118488","https://openalex.org/W2903488900","https://openalex.org/W2050111419","https://openalex.org/W2898988421","https://openalex.org/W3132093802"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,20,26,48,53,145,164,204],"concerned":[3],"with":[4,11],"the":[5,36,71,76,81,102,119,122,126,140,152,185,200,211],"Cauchy":[6],"problem":[7],"$u_{t}=u_{xx}+f(t,u),x\\in":[8],"\\mathbb{R}":[9],",t>0$":[10],"initial":[12,223],"function":[13,149],"$u(0,\\cdot)=u_0":[14],"(\\cdot)\\in":[15],"L^{\\infty}":[16],"(\\mathbb{R})$,":[17],"where":[18,143,202],"$f$":[19,134,203],"a":[21,40,107,111,146,191,205,217],"rather":[22,192],"general":[23,166],"nonlinearity":[24],"that":[25,35,46,50,168,184],"periodic":[27,42],"in":[28,199],"$t$,":[29],"and":[30,34,60,90,104,117,150,213],"satisfies":[31],"$f(\\cdot,0)\\equiv":[32],"0$":[33],"corresponding":[37],"ODE":[38],"has":[39],"positive":[41],"solution":[43,77,123],"$p(t)$.":[44],"Assuming":[45],"$u_0$":[47,144,163],"front-like,":[49],"is,":[51],"$u_0(x)$":[52],"close":[54,61],"to":[55,62,69,125],"$p(0)$":[56],"for":[57,64,110,216],"$x\\approx":[58,65],"-\\infty$":[59],"$0$":[63],"\\infty$,":[66],"we":[67,182,209],"aim":[68],"determine":[70],"long-time":[72],"dynamical":[73],"behavior":[74],"of":[75,83,106,115,121,221],"$u(t,x)$":[78,124],"by":[79,87],"using":[80],"notion":[82],"propagation":[84],"terrace":[85,109,127],"introduced":[86],"Ducrot,":[88],"Giletti,":[89],"Matano":[91],"[Trans.":[92],"Amer.":[93],"Math.":[94],"Soc.":[95],"366":[96],"(2014),":[97],"pp.":[98],"5541--5566].":[99],"We":[100,137],"establish":[101],"existence":[103],"uniqueness":[105],"propagating":[108],"very":[112],"large":[113],"class":[114,220],"nonlinearities":[116],"show":[118,183,210],"convergence":[120,186,215],"as":[128],"$t\\to\\infty$":[129],"under":[130,190],"various":[131],"conditions":[132],"on":[133,159,196],"or":[135],"$u_0$.":[136],"first":[138],"consider":[139],"special":[141],"case":[142,201],"Heaviside":[147,175],"type":[148,176],"prove":[151],"converge":[153],"result":[154,187],"without":[155],"requiring":[156],"any":[157],"nondegeneracy":[158,194],"$f$.":[160,197],"Furthermore,":[161],"if":[162],"more":[165],"such":[167],"it":[169],"can":[170],"be":[171],"trapped":[172],"between":[173],"two":[174],"functions,":[177],"but":[178],"not":[179],"necessarily":[180],"monotone,":[181],"remains":[188],"valid":[189],"mild":[193],"assumption":[195],"Last,":[198],"nondegenerate":[206],"multistable":[207],"nonlinearity,":[208],"global":[212],"exponential":[214],"much":[218],"larger":[219],"front-like":[222],"data.":[224]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-06T13:50:29.536080","created_date":"2025-10-10T00:00:00"}
