{"id":"https://openalex.org/W1537583255","doi":"https://doi.org/10.1137/140969427","title":"Time-Delayed Instabilities in Complex Burgers Equations","display_name":"Time-Delayed Instabilities in Complex Burgers Equations","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1537583255","doi":"https://doi.org/10.1137/140969427","mag":"1537583255"},"language":"en","primary_location":{"id":"doi:10.1137/140969427","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140969427","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/A5017484115","display_name":"Marta Strani","orcid":"https://orcid.org/0000-0003-0818-0950"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Marta Strani","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5041545242","display_name":"Benjamin Texier","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Benjamin Texier","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5017484115"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2556,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.58146381,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"47","issue":"4","first_page":"2495","last_page":"2518"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9919999837875366,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9898999929428101,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8261913061141968},{"id":"https://openalex.org/keywords/burgers-equation","display_name":"Burgers' equation","score":0.7804927825927734},{"id":"https://openalex.org/keywords/forcing","display_name":"Forcing (mathematics)","score":0.7267022132873535},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5361229181289673},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.4988842010498047},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.49245867133140564},{"id":"https://openalex.org/keywords/viscosity","display_name":"Viscosity","score":0.47775307297706604},{"id":"https://openalex.org/keywords/exponential-growth","display_name":"Exponential growth","score":0.47391924262046814},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4587990641593933},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4459279477596283},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4126136004924774},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3649289608001709},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.1973561942577362},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1420280635356903},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11035320162773132}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8261913061141968},{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.7804927825927734},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.7267022132873535},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5361229181289673},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.4988842010498047},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.49245867133140564},{"id":"https://openalex.org/C127172972","wikidata":"https://www.wikidata.org/wiki/Q128709","display_name":"Viscosity","level":2,"score":0.47775307297706604},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.47391924262046814},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4587990641593933},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4459279477596283},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4126136004924774},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3649289608001709},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.1973561942577362},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1420280635356903},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11035320162773132},{"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:10.1137/140969427","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140969427","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:iris.unive.it:10278/3699463","is_oa":false,"landing_page_url":"http://hdl.handle.net/10278/3699463","pdf_url":null,"source":{"id":"https://openalex.org/S4306402336","display_name":"ARCA (Universit\u00e0 Ca' Foscari Venezia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149461666","host_organization_name":"Ca' Foscari University of Venice","host_organization_lineage":["https://openalex.org/I149461666"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W623671459","https://openalex.org/W1580666588","https://openalex.org/W2011250908","https://openalex.org/W2026448930","https://openalex.org/W2065676431"],"related_works":["https://openalex.org/W1487790116","https://openalex.org/W3124916295","https://openalex.org/W2146447767","https://openalex.org/W2022411416","https://openalex.org/W2167530280","https://openalex.org/W3197597876","https://openalex.org/W2564447268","https://openalex.org/W1758988473","https://openalex.org/W1968107836","https://openalex.org/W2038335296"],"abstract_inverted_index":{"For":[0],"Burgers":[1,67],"equations":[2,68],"with":[3,72],"real":[4],"data":[5,25,80],"and":[6,12,75],"complex":[7,77],"forcing":[8],"terms,":[9],"Lerner,":[10],"Morimoto,":[11],"Xu":[13],"[Amer.":[14],"J.":[15],"Math.,":[16],"132":[17],"(2010),":[18],"pp.":[19],"99--123]":[20],"proved":[21],"that":[22,53,65],"only":[23,45],"analytical":[24],"generate":[26,81],"local":[27],"$C^2$":[28],"solutions.":[29],"The":[30],"corresponding":[31],"instabilities,":[32],"however,":[33],"are":[34],"not":[35],"observed":[36],"numerically;":[37],"rather,":[38],"numerical":[39,54],"simulations":[40,92],"show":[41],"an":[42],"exponential":[43],"growth":[44],"after":[46],"a":[47,76],"delay":[48],"in":[49,69,86],"time.":[50],"We":[51],"argue":[52],"diffusion":[55],"is":[56],"responsible":[57],"for":[58,66],"this":[59],"time":[60,87],"delay,":[61],"as":[62],"we":[63],"prove":[64],"the":[70,94],"torus":[71],"small":[73],"viscosity":[74],"forcing,":[78],"oscillating":[79],"solutions":[82],"which":[83],"grow":[84],"linearly":[85],"before":[88],"growing":[89],"exponentially.":[90],"Numerical":[91],"illustrate":[93],"results.":[95]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
