{"id":"https://openalex.org/W7215102478","doi":"https://doi.org/10.48550/arxiv.2609.39444","title":"Bistable pulsating waves with periodic advection: homogenization and sharp speed asymptotics","display_name":"Bistable pulsating waves with periodic advection: homogenization and sharp speed asymptotics","publication_year":2026,"publication_date":"2026-09-30","ids":{"openalex":"https://openalex.org/W7215102478","doi":"https://doi.org/10.48550/arxiv.2609.39444"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.39444","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.39444","pdf_url":"https://arxiv.org/pdf/2609.39444","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.39444","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101451180","display_name":"Weiwei Ding","orcid":"https://orcid.org/0000-0002-5795-8987","observed_orcids":["https://orcid.org/0000-0002-5795-8987"]},"institutions":[{"id":"https://openalex.org/I187400657","display_name":"South China Normal University","ror":"https://ror.org/01kq0pv72","country_code":"CN","type":"education","lineage":["https://openalex.org/I187400657"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ding, Weiwei","raw_affiliation_strings":["School of Mathematical Sciences , South China Normal University , Guangzhou 510631 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , South China Normal University , Guangzhou 510631 , China","institution_ids":["https://openalex.org/I187400657"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5154050221","display_name":"Linfeng Xu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xu, Linfeng","raw_affiliation_strings":["School of Mathematical Sciences and Wu Wen-Tsun Key Laboratory of Mathematics , University of Science and Technology of China , Hefei , Anhui , 230026 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences and Wu Wen-Tsun Key Laboratory of Mathematics , University of Science and Technology of China , Hefei , Anhui , 230026 , China","institution_ids":["https://openalex.org/I126520041"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.75,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.75,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.11349999904632568,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.07090000063180923,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/reaction-diffusion-systems","display_name":"reaction-diffusion systems","score":0.9850000143051147},{"id":"https://openalex.org/keywords/homogenization","display_name":"homogenization","score":0.9819999933242798},{"id":"https://openalex.org/keywords/traveling-waves","display_name":"traveling waves","score":0.828000009059906},{"id":"https://openalex.org/keywords/standing-waves","display_name":"standing waves","score":0.6980000138282776}],"concepts":[{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.835099995136261},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7577999830245972},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6887999773025513},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6366000175476074},{"id":"https://openalex.org/C5072599","wikidata":"https://www.wikidata.org/wiki/Q379788","display_name":"Advection","level":2,"score":0.5666000247001648},{"id":"https://openalex.org/C97292510","wikidata":"https://www.wikidata.org/wiki/Q2304620","display_name":"Bistability","level":2,"score":0.5455999970436096},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.47049999237060547},{"id":"https://openalex.org/C2988173416","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Traveling wave","level":2,"score":0.4422999918460846},{"id":"https://openalex.org/C2986045365","wikidata":"https://www.wikidata.org/wiki/Q1163350","display_name":"Wave speed","level":2,"score":0.41290000081062317},{"id":"https://openalex.org/C44886760","wikidata":"https://www.wikidata.org/wiki/Q1758425","display_name":"Wave propagation","level":2,"score":0.4034000039100647},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.36230000853538513},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3391000032424927},{"id":"https://openalex.org/C146864707","wikidata":"https://www.wikidata.org/wiki/Q382774","display_name":"Internal wave","level":2,"score":0.3305000066757202},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.32910001277923584},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.2939000129699707},{"id":"https://openalex.org/C155940","wikidata":"https://www.wikidata.org/wiki/Q7886967","display_name":"Uniqueness theorem for Poisson's equation","level":3,"score":0.28769999742507935},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.2750000059604645},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.2648000121116638},{"id":"https://openalex.org/C130187892","wikidata":"https://www.wikidata.org/wiki/Q133327","display_name":"Spacetime","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.39444","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.39444","pdf_url":"https://arxiv.org/pdf/2609.39444","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"doi:10.48550/arxiv.2609.39444","doi":"https://doi.org/10.48550/arxiv.2609.39444","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.39444","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.39444","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.39444","pdf_url":"https://arxiv.org/pdf/2609.39444","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G5454041052","display_name":null,"funder_award_id":"12471197","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7354929472","display_name":null,"funder_award_id":"2023B1515020034","funder_id":"https://openalex.org/F4320337111","funder_display_name":"Basic and Applied Basic Research Foundation of Guangdong Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320337111","display_name":"Basic and Applied Basic Research Foundation of Guangdong Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7215102478.pdf","grobid_xml":"https://content.openalex.org/works/W7215102478.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4402769850","https://openalex.org/W4415016527"],"related_works":["https://openalex.org/W2123272709","https://openalex.org/W4321220521","https://openalex.org/W7095177258","https://openalex.org/W7099226489","https://openalex.org/W7100354201","https://openalex.org/W2963713611","https://openalex.org/W2024283307","https://openalex.org/W2093261556","https://openalex.org/W4399598189","https://openalex.org/W2080467492"],"abstract_inverted_index":{"We":[0,78],"study":[1],"bistable":[2],"pulsating":[3,42],"waves":[4,43],"for":[5,44,86,91,120],"reaction-diffusion":[6],"equations":[7],"with":[8,32,123],"general":[9,156],"periodic":[10,128],"advection":[11,129,142],"in":[12,35,68,97,141],"arbitrary":[13,87],"space":[14],"dimension,":[15],"allowing":[16],"the":[17,25,56,69,73,83,98,104,113,139,150,155],"diffusion":[18,125],"matrix":[19],"to":[20,55,149],"be":[21],"nonsymmetric.":[22],"Assuming":[23],"that":[24,131,138,154],"homogenized":[26,57,74,151],"equation":[27],"admits":[28],"a":[29,36],"traveling":[30],"wave":[31,58,84],"nonzero":[33],"speed":[34,85,158],"given":[37],"direction,":[38],"we":[39,111],"construct":[40],"moving":[41,92],"all":[45],"sufficiently":[46],"small":[47],"spatial":[48],"periods":[49],"$L$":[50],"and":[51,64,94,116,126,153],"prove":[52,80],"their":[53],"convergence":[54,65],"as":[59],"$L\\to0^+$.":[60],"The":[61],"existence":[62],"range":[63],"are":[66],"uniform":[67],"propagation":[70,147],"direction":[71],"when":[72],"speeds":[75],"never":[76],"vanish.":[77],"also":[79],"uniqueness":[81,90,96],"of":[82,103],"periods,":[88],"profile":[89],"waves,":[93],"stationary-wave":[95],"standing":[99],"case":[100],"under":[101],"continuity":[102],"competing":[105],"profile.":[106],"For":[107],"spatially":[108],"homogeneous":[109],"reactions,":[110],"derive":[112],"expansion":[114],"$c_L=c_0+Lc_1+O(L^2)$":[115],"an":[117],"explicit":[118],"formula":[119],"$c_1$.":[121],"Examples":[122],"constant":[124],"zero-mean":[127],"show":[130],"$c_1$":[132],"can":[133],"have":[134],"either":[135],"sign,":[136],"demonstrating":[137],"heterogeneity":[140],"may":[143],"accelerate":[144],"or":[145],"decelerate":[146],"relative":[148],"limit":[152],"$O(L)$":[157],"estimate":[159],"is":[160],"sharp.":[161]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-02T00:00:00"}