{"id":"https://openalex.org/W2004018986","doi":"https://doi.org/10.1137/100807156","title":"Front Solutions for Bistable Differential-Difference Equations with Inhomogeneous Diffusion","display_name":"Front Solutions for Bistable Differential-Difference Equations with Inhomogeneous Diffusion","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2004018986","doi":"https://doi.org/10.1137/100807156","mag":"2004018986"},"language":"en","primary_location":{"id":"doi:10.1137/100807156","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100807156","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":"https://stars.library.ucf.edu/facultybib2010/1410","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019436119","display_name":"A. R. Humphries","orcid":"https://orcid.org/0000-0002-5736-1240"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"A. R. Humphries","raw_affiliation_strings":["Department of Mathematics and Statistics, McGill University, Montreal, QC H3A 2K6, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, McGill University, Montreal, QC H3A 2K6, Canada","institution_ids":["https://openalex.org/I5023651"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040332761","display_name":"Brian E. Moore","orcid":"https://orcid.org/0000-0001-7914-1794"},"institutions":[{"id":"https://openalex.org/I106165777","display_name":"University of Central Florida","ror":"https://ror.org/036nfer12","country_code":"US","type":"education","lineage":["https://openalex.org/I106165777"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Brian E. Moore","raw_affiliation_strings":["Department of Mathematics, University of Central Florida, Orlando, FL 32816"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Central Florida, Orlando, FL 32816","institution_ids":["https://openalex.org/I106165777"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012033652","display_name":"Erik S. Van Vleck","orcid":"https://orcid.org/0000-0001-9203-8345"},"institutions":[{"id":"https://openalex.org/I146416000","display_name":"University of Kansas","ror":"https://ror.org/001tmjg57","country_code":"US","type":"education","lineage":["https://openalex.org/I146416000"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Erik S. Van Vleck","raw_affiliation_strings":["Department of Mathematics, University of Kansas, Lawrence, KS 66045"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Kansas, Lawrence, KS 66045","institution_ids":["https://openalex.org/I146416000"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5019436119"],"corresponding_institution_ids":["https://openalex.org/I5023651"],"apc_list":null,"apc_paid":null,"fwci":0.9402,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.78655088,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"71","issue":"4","first_page":"1374","last_page":"1400"},"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":0.9987999796867371,"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":0.9987999796867371,"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":0.998199999332428,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9972000122070312,"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/monotone-polygon","display_name":"Monotone polygon","score":0.6593488454818726},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6305772066116333},{"id":"https://openalex.org/keywords/bistability","display_name":"Bistability","score":0.627230167388916},{"id":"https://openalex.org/keywords/front","display_name":"Front (military)","score":0.5767908692359924},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5733791589736938},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5677259564399719},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5593217611312866},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.4709794521331787},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.46927228569984436},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4614931344985962},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.429232656955719},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21802076697349548},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14471226930618286}],"concepts":[{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6593488454818726},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6305772066116333},{"id":"https://openalex.org/C97292510","wikidata":"https://www.wikidata.org/wiki/Q2304620","display_name":"Bistability","level":2,"score":0.627230167388916},{"id":"https://openalex.org/C2777551076","wikidata":"https://www.wikidata.org/wiki/Q842332","display_name":"Front (military)","level":2,"score":0.5767908692359924},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5733791589736938},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5677259564399719},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5593217611312866},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.4709794521331787},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.46927228569984436},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4614931344985962},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.429232656955719},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21802076697349548},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14471226930618286},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/100807156","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100807156","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:stars.library.ucf.edu:facultybib2010-2409","is_oa":true,"landing_page_url":"https://stars.library.ucf.edu/facultybib2010/1410","pdf_url":null,"source":{"id":"https://openalex.org/S4210172555","display_name":"Journal of International Crisis and Risk Communication Research","issn_l":"2576-0017","issn":["2576-0017","2576-0025"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Bibliography 2010s","raw_type":"text"},{"id":"pmh:oai:kuscholarworks.ku.edu:1808/17245","is_oa":true,"landing_page_url":"http://hdl.handle.net/1808/17245","pdf_url":null,"source":{"id":"https://openalex.org/S4306400421","display_name":"KU ScholarWorks (The University of Kansas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I146416000","host_organization_name":"University of Kansas","host_organization_lineage":["https://openalex.org/I146416000"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:stars.library.ucf.edu:facultybib2010-2409","is_oa":true,"landing_page_url":"https://stars.library.ucf.edu/facultybib2010/1410","pdf_url":null,"source":{"id":"https://openalex.org/S4210172555","display_name":"Journal of International Crisis and Risk Communication Research","issn_l":"2576-0017","issn":["2576-0017","2576-0025"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Bibliography 2010s","raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.5799999833106995,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W186599579","https://openalex.org/W1483675707","https://openalex.org/W1484335179","https://openalex.org/W1589242138","https://openalex.org/W1966058818","https://openalex.org/W1967848725","https://openalex.org/W1968267631","https://openalex.org/W1985314283","https://openalex.org/W1985875536","https://openalex.org/W1992222272","https://openalex.org/W1993693726","https://openalex.org/W2003128769","https://openalex.org/W2011021720","https://openalex.org/W2019984076","https://openalex.org/W2022748003","https://openalex.org/W2022882918","https://openalex.org/W2024174082","https://openalex.org/W2026703542","https://openalex.org/W2040545012","https://openalex.org/W2042102840","https://openalex.org/W2046960180","https://openalex.org/W2055826414","https://openalex.org/W2061749829","https://openalex.org/W2063900463","https://openalex.org/W2069946517","https://openalex.org/W2075182728","https://openalex.org/W2092566320","https://openalex.org/W2101094100","https://openalex.org/W2101495277","https://openalex.org/W2102223767","https://openalex.org/W2108331166","https://openalex.org/W2109384700","https://openalex.org/W2120081882","https://openalex.org/W2122576752","https://openalex.org/W2162931579","https://openalex.org/W2168973270","https://openalex.org/W2324504160","https://openalex.org/W2560896015","https://openalex.org/W3103230865"],"related_works":["https://openalex.org/W3091357103","https://openalex.org/W2953326236","https://openalex.org/W3182827720","https://openalex.org/W1596838019","https://openalex.org/W2133947431","https://openalex.org/W2490196280","https://openalex.org/W3208509670","https://openalex.org/W2100864966","https://openalex.org/W2109304297","https://openalex.org/W2083709218"],"abstract_inverted_index":{"We":[0],"consider":[1],"a":[2,10,91,98,115],"bistable":[3],"differential-difference":[4],"equation":[5],"with":[6,128],"inhomogeneous":[7,62],"diffusion.":[8],"Employing":[9],"piecewise":[11],"linear":[12],"nonlinearity,":[13],"often":[14],"referred":[15],"to":[16,35,47,74],"as":[17,114],"McKean's":[18],"caricature":[19],"of":[20,32,44,72,83,94,110,117,123,131],"the":[21,30,42,70,75,107,118,124,129],"cubic,":[22],"we":[23],"construct":[24],"front":[25,38,49,112],"solutions":[26,39,73,113],"which":[27],"correspond,":[28],"in":[29,41,88,102],"case":[31,43,82],"homogeneous":[33],"diffusion,":[34,64],"monotone":[36],"traveling":[37],"or,":[40],"propagation":[45,95],"failure,":[46],"stationary":[48],"solutions.":[50],"A":[51],"general":[52],"form":[53],"for":[54,59,69],"these":[55,111],"fronts":[56],"is":[57,86,126],"given":[58,68],"essentially":[60],"arbitrary":[61],"discrete":[63,77],"and":[65,97,120],"conditions":[66],"are":[67],"existence":[71],"original":[76],"Nagumo":[78],"equation.":[79],"The":[80],"specific":[81],"one":[84],"defect":[85],"considered":[87],"depth,":[89],"giving":[90],"complete":[92],"understanding":[93],"failure":[96],"grasp":[99],"on":[100],"changes":[101],"wave":[103],"speed.":[104],"Insight":[105],"into":[106],"dynamic":[108],"behavior":[109],"function":[116],"magnitude":[119],"relative":[121],"position":[122],"defects":[125],"obtained":[127],"assistance":[130],"numerical":[132],"results.":[133]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}