{"id":"https://openalex.org/W1135526296","doi":"https://doi.org/10.3233/asy-141281","title":"Parabolic problems in R n with spatially variable exponents","display_name":"Parabolic problems in R n with spatially variable exponents","publication_year":2015,"publication_date":"2015-06-12","ids":{"openalex":"https://openalex.org/W1135526296","doi":"https://doi.org/10.3233/asy-141281","mag":"1135526296"},"language":"en","primary_location":{"id":"doi:10.3233/asy-141281","is_oa":false,"landing_page_url":"https://doi.org/10.3233/asy-141281","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/A5004270706","display_name":"Claudianor O. Alves","orcid":"https://orcid.org/0000-0001-6921-7548"},"institutions":[{"id":"https://openalex.org/I41455075","display_name":"Universidade Federal de Campina Grande","ror":"https://ror.org/00eftnx64","country_code":"BR","type":"education","lineage":["https://openalex.org/I41455075"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Claudianor O. Alves","raw_affiliation_strings":["Unidade Acad\u00eamica de Matem\u00e1tica, Universidade Federal de Campina Grande, Campina Grande, PB, Brazil. E-mail:\u00a0coalvesbr@yahoo.com.br"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Unidade Acad\u00eamica de Matem\u00e1tica, Universidade Federal de Campina Grande, Campina Grande, PB, Brazil. E-mail:\u00a0coalvesbr@yahoo.com.br","institution_ids":["https://openalex.org/I41455075"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069175255","display_name":"Jacson Simsen","orcid":"https://orcid.org/0000-0002-6683-1363"},"institutions":[{"id":"https://openalex.org/I8165072","display_name":"Universidade Federal de Itajub\u00e1","ror":"https://ror.org/00235nr42","country_code":"BR","type":"education","lineage":["https://openalex.org/I8165072"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Jacson Simsen","raw_affiliation_strings":["Instituto de Matem\u00e1tica e Computa\u00e7\u00e3o, Universidade Federal de Itajub\u00e1, Itajub\u00e1, MG, Brazil. E-mails:\u00a0jacson@unifei.edu.br,\u00a0mariza@unifei.edu.br"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica e Computa\u00e7\u00e3o, Universidade Federal de Itajub\u00e1, Itajub\u00e1, MG, Brazil. E-mails:\u00a0jacson@unifei.edu.br,\u00a0mariza@unifei.edu.br","institution_ids":["https://openalex.org/I8165072"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052783073","display_name":"Mariza Stefanello Simsen","orcid":"https://orcid.org/0000-0002-2378-2442"},"institutions":[{"id":"https://openalex.org/I8165072","display_name":"Universidade Federal de Itajub\u00e1","ror":"https://ror.org/00235nr42","country_code":"BR","type":"education","lineage":["https://openalex.org/I8165072"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Mariza S. Simsen","raw_affiliation_strings":["Instituto de Matem\u00e1tica e Computa\u00e7\u00e3o, Universidade Federal de Itajub\u00e1, Itajub\u00e1, MG, Brazil. E-mails:\u00a0jacson@unifei.edu.br,\u00a0mariza@unifei.edu.br"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica e Computa\u00e7\u00e3o, Universidade Federal de Itajub\u00e1, Itajub\u00e1, MG, Brazil. E-mails:\u00a0jacson@unifei.edu.br,\u00a0mariza@unifei.edu.br","institution_ids":["https://openalex.org/I8165072"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5069175255"],"corresponding_institution_ids":["https://openalex.org/I8165072"],"apc_list":{"value":4150,"currency":"USD","value_usd":4150},"apc_paid":null,"fwci":0.6728,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.71516698,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"93","issue":"1-2","first_page":"51","last_page":"64"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9998000264167786,"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":0.9998000264167786,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9986000061035156,"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/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.6687346696853638},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5728487968444824},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.46518391370773315},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.464266300201416},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4574126899242401},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4303857982158661},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4189053773880005},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3833152651786804},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37529611587524414},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.13486501574516296}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6687346696853638},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5728487968444824},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.46518391370773315},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.464266300201416},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4574126899242401},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4303857982158661},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4189053773880005},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3833152651786804},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37529611587524414},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.13486501574516296},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/asy-141281","is_oa":false,"landing_page_url":"https://doi.org/10.3233/asy-141281","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W34271111","https://openalex.org/W61514442","https://openalex.org/W217815568","https://openalex.org/W1582617215","https://openalex.org/W1594759473","https://openalex.org/W1607530402","https://openalex.org/W2018035406","https://openalex.org/W2034690464","https://openalex.org/W2046851382","https://openalex.org/W2047766644","https://openalex.org/W2313692227","https://openalex.org/W2724441196","https://openalex.org/W2964044182","https://openalex.org/W4292366025","https://openalex.org/W6608758421","https://openalex.org/W6740235934"],"related_works":["https://openalex.org/W3185235544","https://openalex.org/W2911623553","https://openalex.org/W4297791327","https://openalex.org/W2897842840","https://openalex.org/W2397777611","https://openalex.org/W1502031429","https://openalex.org/W2417585376","https://openalex.org/W1994157709","https://openalex.org/W4294336468","https://openalex.org/W2797811993"],"abstract_inverted_index":{"We":[0,50],"study":[1,52],"the":[2,10,53,56,60,63],"asymptotic":[3],"behavior":[4],"of":[5,9,55,62],"parabolic":[6],"p(x)-Laplacian":[7],"problems":[8],"form":[11],"\u2202u\u03bb\u2202t\u2212div(D\u03bb|\u2207u\u03bb|p(x)\u22122\u2207u\u03bb)+a|u\u03bb|p(x)\u22122u\u03bb=B(u\u03bb)":[12],"in":[13,23],"L2(Rn),":[14],"where":[15],"n\u2a7e1,":[16],"p\u2208L\u221e(Rn)":[17],"such":[18,40],"that":[19,41],"2":[20],"M\u2a7eD\u03bb(x)\u2a7e\u03c3>0":[21],"a.e.":[22],"Rn,":[24],"\u03bb\u2208[0,\u221e),":[25],"B:L2(Rn)\u2192L2(Rn)":[26],"is":[27,35],"a":[28,36],"glo":[29],"bally":[30],"Lipschitz":[31],"map":[32],"and":[33,48],"a:Rn\u2192R":[34],"non-negative":[37],"continuous":[38],"function":[39],"there":[42],"exists":[43],"R1>0":[44],"with":[45],"{x\u2208Rn;a(x)=0}\u2282BR1(0),":[46],"infx\u2208Rn\u2216BR1(0)a(x)>0,":[47],"\u222bRn\u2216BR1(0)1a(x)2/(p(x)\u22122)dx<+\u221e.":[49],"also":[51],"sensitivity":[54],"problem":[57],"according":[58],"to":[59],"variation":[61],"diffusion":[64],"coefficients.":[65]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}