{"id":"https://openalex.org/W2017573239","doi":"https://doi.org/10.1137/100819527","title":"A Singular Hamilton--Jacobi Equation Modeling the Tail Problem","display_name":"A Singular Hamilton--Jacobi Equation Modeling the Tail Problem","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2017573239","doi":"https://doi.org/10.1137/100819527","mag":"2017573239"},"language":"en","primary_location":{"id":"doi:10.1137/100819527","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100819527","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":true,"oa_status":"green","oa_url":"https://hal.science/hal-00503154","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085283703","display_name":"Sepideh Mirrahimi","orcid":"https://orcid.org/0000-0002-6396-6123"},"institutions":[{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Sepideh Mirrahimi","raw_affiliation_strings":["LJLL - Laboratoire Jacques-Louis Lions (Universit\u00e9 Pierre et Marie Curie, Bo\u00eete courrier 187 - 75252 Paris Cedex 05 - France)"],"affiliations":[{"raw_affiliation_string":"LJLL - Laboratoire Jacques-Louis Lions (Universit\u00e9 Pierre et Marie Curie, Bo\u00eete courrier 187 - 75252 Paris Cedex 05 - France)","institution_ids":["https://openalex.org/I4210158291"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016430930","display_name":"Guy Barles","orcid":"https://orcid.org/0000-0001-9381-4676"},"institutions":[{"id":"https://openalex.org/I4210132217","display_name":"Laboratoire de Math\u00e9matiques et Physique Th\u00e9orique","ror":"https://ror.org/03g2c2k71","country_code":"FR","type":"facility","lineage":["https://openalex.org/I110017253","https://openalex.org/I1294671590","https://openalex.org/I4210132217","https://openalex.org/I4210141950"]},{"id":"https://openalex.org/I4210131315","display_name":"Laboratoire de Math\u00e9matiques Analyse, Probabilit\u00e9s, Mod\u00e9lisation Orl\u00e9ans","ror":"https://ror.org/03d6rdf69","country_code":"FR","type":"facility","lineage":["https://openalex.org/I12449238","https://openalex.org/I1294671590","https://openalex.org/I4210131315","https://openalex.org/I4210141950"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Guy Barles","raw_affiliation_strings":["FDP - F\u00e9d\u00e9ration de recherche Denis Poisson (Laboratoire MAPMO rue de Chartres B\u00e2t. Maths. - 6759 - 45067 ORLEANS CEDEX 2 - France)","LMPT - Laboratoire de Math\u00e9matiques et Physique Th\u00e9orique (Avenue Monge Parc de Grandmont - 37200 Tours - France)"],"affiliations":[{"raw_affiliation_string":"FDP - F\u00e9d\u00e9ration de recherche Denis Poisson (Laboratoire MAPMO rue de Chartres B\u00e2t. Maths. - 6759 - 45067 ORLEANS CEDEX 2 - France)","institution_ids":["https://openalex.org/I4210131315"]},{"raw_affiliation_string":"LMPT - Laboratoire de Math\u00e9matiques et Physique Th\u00e9orique (Avenue Monge Parc de Grandmont - 37200 Tours - France)","institution_ids":["https://openalex.org/I4210132217"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061988258","display_name":"Beno\u0131\u0302t Perthame","orcid":"https://orcid.org/0000-0002-7091-1200"},"institutions":[{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Beno\u00eet Perthame","raw_affiliation_strings":["LJLL - Laboratoire Jacques-Louis Lions (Universit\u00e9 Pierre et Marie Curie, Bo\u00eete courrier 187 - 75252 Paris Cedex 05 - France)","BANG - Nonlinear Analysis for Biology and Geophysical flows (Domaine de Voluceau ; BP 105 ; 78150 Rocquencourt - France)"],"affiliations":[{"raw_affiliation_string":"LJLL - Laboratoire Jacques-Louis Lions (Universit\u00e9 Pierre et Marie Curie, Bo\u00eete courrier 187 - 75252 Paris Cedex 05 - France)","institution_ids":["https://openalex.org/I4210158291"]},{"raw_affiliation_string":"BANG - Nonlinear Analysis for Biology and Geophysical flows (Domaine de Voluceau ; BP 105 ; 78150 Rocquencourt - France)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066466020","display_name":"Panagiotis E. Souganidis","orcid":"https://orcid.org/0000-0003-2399-0759"},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Panagiotis E. Souganidis","raw_affiliation_strings":["Department of Mathematics (5734 S. University Avenue, Chicago, IL 60637, USA. - United States)"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics (5734 S. University Avenue, Chicago, IL 60637, USA. - United States)","institution_ids":["https://openalex.org/I40347166"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5085283703"],"corresponding_institution_ids":["https://openalex.org/I4210158291"],"apc_list":null,"apc_paid":null,"fwci":0.5041,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.63023308,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"44","issue":"6","first_page":"4297","last_page":"4319"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9973000288009644,"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/T11764","display_name":"Evolution and Genetic Dynamics","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8394532203674316},{"id":"https://openalex.org/keywords/singular-control","display_name":"Singular control","score":0.5380347371101379},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5243954062461853},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5003213882446289},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.494354248046875},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.4797400236129761},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.45712345838546753},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.4538527727127075},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4416097402572632},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.4134593605995178},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.17560458183288574},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.14841094613075256}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8394532203674316},{"id":"https://openalex.org/C2777984672","wikidata":"https://www.wikidata.org/wiki/Q7524238","display_name":"Singular control","level":3,"score":0.5380347371101379},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5243954062461853},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5003213882446289},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.494354248046875},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.4797400236129761},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.45712345838546753},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.4538527727127075},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4416097402572632},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.4134593605995178},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.17560458183288574},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.14841094613075256},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/100819527","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100819527","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:HAL:hal-00503154v2","is_oa":true,"landing_page_url":"https://hal.science/hal-00503154","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 Mathematical Analysis, 2012, 44 (6), pp.4297-4319. &#x27E8;10.1137/100819527&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00503154v2","is_oa":true,"landing_page_url":"https://hal.science/hal-00503154","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 Mathematical Analysis, 2012, 44 (6), pp.4297-4319. &#x27E8;10.1137/100819527&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[{"display_name":"Good health and well-being","score":0.800000011920929,"id":"https://metadata.un.org/sdg/3"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W76589213","https://openalex.org/W573861537","https://openalex.org/W1487586009","https://openalex.org/W1505284970","https://openalex.org/W1532111732","https://openalex.org/W1588370453","https://openalex.org/W1979851842","https://openalex.org/W2022119271","https://openalex.org/W2029188814","https://openalex.org/W2032316144","https://openalex.org/W2044960635","https://openalex.org/W2063152565","https://openalex.org/W2124348374","https://openalex.org/W2141616022","https://openalex.org/W2145770111","https://openalex.org/W2749408143","https://openalex.org/W2963570066","https://openalex.org/W3105662858","https://openalex.org/W4249975767","https://openalex.org/W4251046712","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W4301247218","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W2129818458","https://openalex.org/W4289551052","https://openalex.org/W4302167439","https://openalex.org/W2271170716","https://openalex.org/W2891289036"],"abstract_inverted_index":{"We":[0,85],"study":[1,208],"the":[2,8,22,29,37,49,52,68,77,100,108,119,140,145,149,181,211,225,228,234,239,244],"asymptotic":[3],"(long-time/long-range)":[4],"exponential":[5,120,193],"behavior":[6,30,121],"of":[7,36,39,51,64,137,163,214],"solutions":[9],"to":[10,21,60,103,190,196],"reaction-diffusion":[11,88],"equations":[12],"with":[13,56,67,81],"negative":[14],"square":[15,53],"root--type":[16],"reaction":[17],"terms.":[18],"In":[19],"contrast":[20],"classical":[23],"cases,":[24],"for":[25,44,139],"example,":[26],"KPP-type":[27],"nonlinearities,":[28],"is":[31,195,219,231,247],"not":[32,112],"described":[33],"in":[34,71,123,185,224,238],"terms":[35],"solution":[38,78],"a":[40,45,57,61,72,87,92,134,159,198,203],"standard":[41],"obstacle":[42],"problem":[43,184],"Hamilton--Jacobi":[46],"equation.":[47],"Instead":[48],"combination":[50],"root":[54],"term":[55,110,218,246],"threshold":[58,236],"leads":[59],"new":[62],"type":[63,165],"quasi-variational":[65,105,141],"inequality":[66,142],"equation":[69,89],"holding":[70],"domain":[73],"which":[74],"depends":[75],"on":[76,99,144,148],"itself":[79],"and":[80,96,129,154,169,222],"state-constraint":[82,155],"boundary":[83,156],"conditions.":[84],"consider":[86],"involving":[90],"only":[91,127],"linear":[93],"competition":[94,109,245],"term,":[95],"we":[97,115,125],"concentrate":[98],"difficulty":[101],"related":[102],"this":[104,164,215],"inequality.":[106],"When":[107],"does":[111],"change":[113],"sign,":[114],"can":[116],"completely":[117],"identify":[118],"while,":[122],"general,":[124],"obtain":[126],"lower":[128],"upper":[130],"bounds.":[131],"Counterexamples":[132],"show":[133],"nontrivial":[135],"lack":[136],"uniqueness":[138],"depending":[143],"conditions":[146,157],"imposed":[147],"free":[150],"boundary.":[151],"Both":[152],"Dirichlet":[153],"play":[158],"role.":[160],"Although":[161],"models":[162],"are":[166,172],"rather":[167],"old":[168],"extinction":[170],"phenomena":[171],"as":[173,175],"important":[174],"blow-up,":[176],"our":[177],"motivation":[178],"comes":[179],"from":[180],"so-called":[182],"tail":[183],"population":[186,229],"biology.":[187],"One":[188],"way":[189],"avoid":[191],"meaningless":[192],"tails":[194],"impose":[197],"singular":[199,216],"mortality":[200,217],"rate":[201],"below":[202],"given":[204],"survival":[205,226,235],"threshold.":[206],"Our":[207],"shows":[209],"that":[210],"precise":[212],"form":[213],"asymptotically":[220],"irrelevant":[221],"that,":[223],"zone,":[227],"profile":[230],"impacted":[232],"by":[233],"(except":[237],"very":[240],"particular":[241],"case":[242],"when":[243],"nonpositive).":[248]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
