{"id":"https://openalex.org/W2048279040","doi":"https://doi.org/10.1137/s0036141098346785","title":"Global Asymptotic Stability of Traveling Waves in Delayed Reaction-Diffusion Equations","display_name":"Global Asymptotic Stability of Traveling Waves in Delayed Reaction-Diffusion Equations","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2048279040","doi":"https://doi.org/10.1137/s0036141098346785","mag":"2048279040"},"language":"en","primary_location":{"id":"doi:10.1137/s0036141098346785","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141098346785","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/A5109396218","display_name":"Hal L. Smith","orcid":null},"institutions":[{"id":"https://openalex.org/I4210152479","display_name":"Statistical Service","ror":"https://ror.org/05vydvf11","country_code":"CY","type":"government","lineage":["https://openalex.org/I4210152479"]}],"countries":["CY"],"is_corresponding":false,"raw_author_name":"Hal L. Smith","raw_affiliation_strings":["CLAS-NS: Mathematics and Statistical Sciences, School of (SMSS)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CLAS-NS: Mathematics and Statistical Sciences, School of (SMSS)","institution_ids":["https://openalex.org/I4210152479"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108578833","display_name":"Xiao\u2010Qiang Zhao","orcid":"https://orcid.org/0000-0002-3026-2656"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiao-Qiang Zhao","raw_affiliation_strings":["Arizona State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Arizona State University","institution_ids":["https://openalex.org/I55732556"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4202,"has_fulltext":false,"cited_by_count":235,"citation_normalized_percentile":{"value":0.72520211,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"31","issue":"3","first_page":"514","last_page":"534"},"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":0.9988999962806702,"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":0.9988999962806702,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9959999918937683,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9959999918937683,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8726261854171753},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7273684144020081},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.7190702557563782},{"id":"https://openalex.org/keywords/traveling-wave","display_name":"Traveling wave","score":0.7153575420379639},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.7119508385658264},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6531651616096497},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.6312394142150879},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5876064300537109},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5050848126411438},{"id":"https://openalex.org/keywords/comparison-theorem","display_name":"Comparison theorem","score":0.4959748685359955},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4576098620891571},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.10348793864250183},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10316392779350281},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07483017444610596}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8726261854171753},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7273684144020081},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.7190702557563782},{"id":"https://openalex.org/C2988173416","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Traveling wave","level":2,"score":0.7153575420379639},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.7119508385658264},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6531651616096497},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.6312394142150879},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5876064300537109},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5050848126411438},{"id":"https://openalex.org/C2779396167","wikidata":"https://www.wikidata.org/wiki/Q5156040","display_name":"Comparison theorem","level":2,"score":0.4959748685359955},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4576098620891571},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10348793864250183},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10316392779350281},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07483017444610596},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036141098346785","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141098346785","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:10.1.1.556.8999","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.556.8999","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://math.la.asu.edu/~halsmith/wave.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W47407836","https://openalex.org/W1506727362","https://openalex.org/W1527296550","https://openalex.org/W1583311599","https://openalex.org/W1583602735","https://openalex.org/W1605753492","https://openalex.org/W1851248039","https://openalex.org/W1975185802","https://openalex.org/W1992079617","https://openalex.org/W2002055895","https://openalex.org/W2005175928","https://openalex.org/W2009710695","https://openalex.org/W2020718248","https://openalex.org/W2034790369","https://openalex.org/W2047926127","https://openalex.org/W2067831736","https://openalex.org/W2075182728","https://openalex.org/W2081827062","https://openalex.org/W2109011963"],"related_works":["https://openalex.org/W1976743368","https://openalex.org/W2061818987","https://openalex.org/W1997022868","https://openalex.org/W2058973986","https://openalex.org/W4287780914","https://openalex.org/W3034862729","https://openalex.org/W3013945958","https://openalex.org/W3023599262","https://openalex.org/W2064520184","https://openalex.org/W1970842439"],"abstract_inverted_index":{"Key":[0],"words.":[1],"Delayed":[2],"reaction-diffusion":[3,33],"equations,":[4],"comparison":[5,22,67],"principle,":[6],"super-":[7,64],"and":[8,21,52,65,68],"sub-solutions,":[9],"traveling":[10,55],"waves.":[11],"AMS(MOS)":[12],"Subject":[13],"Classifications:":[14],"35R10,":[15],"35B40,":[16],"34K30,":[17],"58D25.":[18],"The":[19,46],"existence":[20],"theorem":[23],"of":[24,41,54],"solutions":[25,57],"is":[26],"first":[27],"estab-lished":[28],"for":[29],"the":[30,39,62],"quasimonotone":[31],"delayed":[32],"equations":[34],"onR":[35],"by":[36,61],"appealing":[37],"to":[38],"theory":[40],"abstract":[42],"functional":[43],"differential":[44],"equations.":[45],"global":[47],"asymptotic":[48],"stability,":[49],"Liapunov":[50],"stability":[51],"uniqueness":[53],"wave":[56],"are":[58],"then":[59],"proved":[60],"elementary":[63],"sub-solution":[66],"squeezing":[69],"methods.":[70]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":13},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":16},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":13},{"year":2020,"cited_by_count":13},{"year":2019,"cited_by_count":15},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":17},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":16},{"year":2014,"cited_by_count":11},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}