{"id":"https://openalex.org/W2979545883","doi":"https://doi.org/10.1137/19m1292187","title":"Quantitative Estimates of the Threshold Phenomena for Propagation in Reaction-Diffusion Equations","display_name":"Quantitative Estimates of the Threshold Phenomena for Propagation in Reaction-Diffusion Equations","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2979545883","doi":"https://doi.org/10.1137/19m1292187","mag":"2979545883"},"language":"en","primary_location":{"id":"doi:10.1137/19m1292187","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1292187","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Dynamical Systems","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1910.04016","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012220090","display_name":"Matthieu Alfaro","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Matthieu Alfaro","raw_affiliation_strings":["IMAG"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMAG","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111055166","display_name":"Arnaud Ducrot","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Arnaud Ducrot","raw_affiliation_strings":["LMAH"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LMAH","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015702631","display_name":"Gr\u00e9gory Faye","orcid":"https://orcid.org/0000-0001-7390-4295"},"institutions":[{"id":"https://openalex.org/I84500057","display_name":"Institut de Math\u00e9matiques de Toulouse","ror":"https://ror.org/014vp6c30","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I196454796","https://openalex.org/I4210092408","https://openalex.org/I4210126056","https://openalex.org/I4210141950","https://openalex.org/I4210152422","https://openalex.org/I4405258862","https://openalex.org/I84500057"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Gr\u00e9gory Faye","raw_affiliation_strings":["Institut de Math\u00e9matiques de Toulouse (UMR5219)"],"raw_orcid":"https://orcid.org/0000-0001-7390-4295","affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Toulouse (UMR5219)","institution_ids":["https://openalex.org/I84500057"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00402768,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"2","first_page":"1291","last_page":"1311"},"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":0.9980000257492065,"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":0.9980000257492065,"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":0.9970999956130981,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/bistability","display_name":"Bistability","score":0.7737159729003906},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.7053931355476379},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.610663890838623},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.6011251211166382},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5262624025344849},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5123923420906067},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.46265608072280884},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.45699140429496765},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.41790422797203064},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4107235074043274},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39076393842697144},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3272705078125},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3214903771877289},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.28200846910476685},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.15627282857894897},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.0849335789680481},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.08251461386680603},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.08116796612739563}],"concepts":[{"id":"https://openalex.org/C97292510","wikidata":"https://www.wikidata.org/wiki/Q2304620","display_name":"Bistability","level":2,"score":0.7737159729003906},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.7053931355476379},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.610663890838623},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.6011251211166382},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5262624025344849},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5123923420906067},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.46265608072280884},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.45699140429496765},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.41790422797203064},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4107235074043274},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39076393842697144},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3272705078125},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3214903771877289},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.28200846910476685},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.15627282857894897},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0849335789680481},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.08251461386680603},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.08116796612739563},{"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/19m1292187","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1292187","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1910.04016","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1910.04016","pdf_url":"https://arxiv.org/pdf/1910.04016","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"mag:2979545883","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1910.04016.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:HAL:hal-02308673v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02308673","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"SIAM Journal on Applied Dynamical Systems, 2020, 19 (2), pp.1291-1311. ⟨10.1137/19M1292187⟩","raw_type":"Journal articles"},{"id":"doi:10.48550/arxiv.1910.04016","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1910.04016","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1910.04016","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1910.04016","pdf_url":"https://arxiv.org/pdf/1910.04016","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":[],"awards":[{"id":"https://openalex.org/G1166658832","display_name":"MUSE","funder_award_id":"ANR-16-IDEX-0006","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G406439973","display_name":null,"funder_award_id":"170544IA","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1560147673","https://openalex.org/W1693068537","https://openalex.org/W1966264429","https://openalex.org/W1985113543","https://openalex.org/W1995256812","https://openalex.org/W1999930428","https://openalex.org/W2014863630","https://openalex.org/W2020718248","https://openalex.org/W2024220343","https://openalex.org/W2026102289","https://openalex.org/W2059043933","https://openalex.org/W2072553848","https://openalex.org/W2126766821","https://openalex.org/W2132099746","https://openalex.org/W2207223089","https://openalex.org/W2558631876","https://openalex.org/W2963221075","https://openalex.org/W2963597480","https://openalex.org/W3100239950"],"related_works":["https://openalex.org/W3100239950","https://openalex.org/W2236944626","https://openalex.org/W2092114548","https://openalex.org/W2951577620","https://openalex.org/W2018698233","https://openalex.org/W2561036422","https://openalex.org/W2885829574","https://openalex.org/W3186911925","https://openalex.org/W2802129401","https://openalex.org/W3105037735","https://openalex.org/W3011729516","https://openalex.org/W3043441698","https://openalex.org/W1991874034","https://openalex.org/W1939601086","https://openalex.org/W2141610220","https://openalex.org/W2904481897","https://openalex.org/W2063479115","https://openalex.org/W2963317677","https://openalex.org/W2795963430","https://openalex.org/W1967540885"],"abstract_inverted_index":{"We":[0],"focus":[1],"on":[2,33],"the":[3,20,28,34,54,63],"(sharp)":[4,35],"threshold":[5,36],"phenomena":[6],"arising":[7],"in":[8,53],"some":[9,14,45],"reaction-diffusion":[10],"equations":[11],"supplemented":[12],"with":[13],"compactly":[15],"supported":[16],"initial":[17],"data.":[18],"In":[19],"so-called":[21],"ignition":[22],"and":[23],"bistable":[24],"cases,":[25],"we":[26,49],"prove":[27],"first":[29],"sharp":[30],"quantitative":[31],"estimate":[32],"values.":[37],"Furthermore,":[38],"numerical":[39],"explorations":[40],"allow":[41],"us":[42],"to":[43],"conjecture":[44],"refined":[46],"estimates.":[47],"Last":[48],"provide":[50],"related":[51],"results":[52],"case":[55],"of":[56],"a":[57],"degenerate":[58],"monostable":[59],"nonlinearity":[60],"\u201cnot":[61],"enjoying":[62],"hair":[64],"trigger":[65],"effect.\u201d":[66]},"counts_by_year":[],"updated_date":"2026-07-01T08:55:40.977307","created_date":"2025-10-10T00:00:00"}