{"id":"https://openalex.org/W1731882074","doi":"https://doi.org/10.3233/asy-2008-0925","title":"Stochastic homogenization of quasilinear PDEs with a spatial degeneracy","display_name":"Stochastic homogenization of quasilinear PDEs with a spatial degeneracy","publication_year":2009,"publication_date":"2009-02-01","ids":{"openalex":"https://openalex.org/W1731882074","doi":"https://doi.org/10.3233/asy-2008-0925","mag":"1731882074"},"language":"en","primary_location":{"id":"doi:10.3233/asy-2008-0925","is_oa":false,"landing_page_url":"https://doi.org/10.3233/asy-2008-0925","pdf_url":null,"source":{"id":"https://openalex.org/S141283892","display_name":"Asymptotic Analysis","issn_l":"0921-7134","issn":["0921-7134","1875-8576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asymptotic 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/A5053452011","display_name":"Fran\u00e7ois Delarue","orcid":"https://orcid.org/0000-0002-5511-1088"},"institutions":[{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I3017942884","display_name":"Institut de Math\u00e9matiques de Jussieu-Paris Rive Gauche","ror":"https://ror.org/03fk87k11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I4210141950"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Fran\u00e7ois Delarue","raw_affiliation_strings":["LPMA, Universit\u00e9 Diderot Paris 7, UFR de Math\u00e9matiques, Case 7012, 2, Place Jussieu, 75251 Paris Cedex 05, France. E-mail: delarue@math.jussieu.fr"],"affiliations":[{"raw_affiliation_string":"LPMA, Universit\u00e9 Diderot Paris 7, UFR de Math\u00e9matiques, Case 7012, 2, Place Jussieu, 75251 Paris Cedex 05, France. E-mail: delarue@math.jussieu.fr","institution_ids":["https://openalex.org/I3017942884","https://openalex.org/I204730241"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034900342","display_name":"R\u00e9mi Rhodes","orcid":null},"institutions":[{"id":"https://openalex.org/I56435720","display_name":"Universit\u00e9 Paris Dauphine-PSL","ror":"https://ror.org/052bz7812","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580","https://openalex.org/I56435720"]},{"id":"https://openalex.org/I171048554","display_name":"Centre de Recherche en Math\u00e9matiques de la D\u00e9cision","ror":"https://ror.org/03s0gj002","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I171048554","https://openalex.org/I2746051580","https://openalex.org/I4210141950","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"R\u00e9mi Rhodes","raw_affiliation_strings":["CEREMADE, Universit\u00e9 Paris Dauphine, Place du marc\u00e9chal De Lattre de Tassigny, 75775 Paris Cedex 16, France. E-mail: rhodes@ceremade.dauphine.fr"],"affiliations":[{"raw_affiliation_string":"CEREMADE, Universit\u00e9 Paris Dauphine, Place du marc\u00e9chal De Lattre de Tassigny, 75775 Paris Cedex 16, France. E-mail: rhodes@ceremade.dauphine.fr","institution_ids":["https://openalex.org/I171048554","https://openalex.org/I56435720"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5053452011"],"corresponding_institution_ids":["https://openalex.org/I204730241","https://openalex.org/I3017942884"],"apc_list":null,"apc_paid":null,"fwci":0.6855,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.68065671,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"61","issue":"2","first_page":"61","last_page":"90"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9962000250816345,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/homogenization","display_name":"Homogenization (climate)","score":0.8615583181381226},{"id":"https://openalex.org/keywords/degeneracy","display_name":"Degeneracy (biology)","score":0.7524694204330444},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6193242073059082},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6068522930145264},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.603096604347229},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5706697106361389},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.558243989944458},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5536101460456848},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.41266074776649475},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3711804747581482},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19352081418037415},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06835943460464478}],"concepts":[{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.8615583181381226},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.7524694204330444},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6193242073059082},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6068522930145264},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.603096604347229},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5706697106361389},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.558243989944458},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5536101460456848},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.41266074776649475},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3711804747581482},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19352081418037415},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06835943460464478},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.0},{"id":"https://openalex.org/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/asy-2008-0925","is_oa":false,"landing_page_url":"https://doi.org/10.3233/asy-2008-0925","pdf_url":null,"source":{"id":"https://openalex.org/S141283892","display_name":"Asymptotic Analysis","issn_l":"0921-7134","issn":["0921-7134","1875-8576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asymptotic Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W158490233","https://openalex.org/W172603095","https://openalex.org/W320338864","https://openalex.org/W582939420","https://openalex.org/W1496526657","https://openalex.org/W1547403762","https://openalex.org/W1556159002","https://openalex.org/W1582610265","https://openalex.org/W1589236075","https://openalex.org/W1601374005","https://openalex.org/W1963852224","https://openalex.org/W1974309308","https://openalex.org/W1986379750","https://openalex.org/W2028970490","https://openalex.org/W2044012760","https://openalex.org/W2072685235","https://openalex.org/W2148116521","https://openalex.org/W2148264639","https://openalex.org/W2231106691","https://openalex.org/W2796487845","https://openalex.org/W3091814460","https://openalex.org/W4213427019","https://openalex.org/W4249303611"],"related_works":["https://openalex.org/W2125277162","https://openalex.org/W1552514155","https://openalex.org/W168460013","https://openalex.org/W4287687395","https://openalex.org/W2215112080","https://openalex.org/W3037733829","https://openalex.org/W4300428659","https://openalex.org/W2036979411","https://openalex.org/W4292881691","https://openalex.org/W2955288804"],"abstract_inverted_index":{"We":[0],"investigate":[1],"stochastic":[2],"homogenization":[3,53],"for":[4,55],"some":[5],"degenerate":[6],"quasilinear":[7,57],"parabolic":[8],"PDEs.":[9],"The":[10,66],"underlying":[11],"nonlinear":[12,22],"operator":[13,36,46,69],"degenerates":[14],"along":[15],"the":[16,21,24,29,38,52,56,62],"space":[17],"variable,":[18],"uniformly":[19],"in":[20],"term:":[23],"degeneracy":[25,30],"points":[26,31],"correspond":[27],"to":[28],"of":[32,61],"a":[33],"reference":[34,44],"diffusion":[35,45],"on":[37],"random":[39],"medium.":[40],"Assuming":[41],"that":[42],"this":[43],"is":[47],"ergodic,":[48],"we":[49],"can":[50],"prove":[51],"property":[54],"PDEs,":[58],"by":[59],"means":[60],"first-order":[63],"approximation":[64],"method.":[65],"(nonlinear)":[67],"limit":[68],"need":[70],"not":[71],"be":[72],"nondegenerate.":[73],"Concrete":[74],"examples":[75],"are":[76],"provided.":[77]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
