{"id":"https://openalex.org/W4376142003","doi":"https://doi.org/10.1080/00036811.2023.2208126","title":"Well-posedness and exponential stability of coupled non-degenerate Kirchhoff and heat equations","display_name":"Well-posedness and exponential stability of coupled non-degenerate Kirchhoff and heat equations","publication_year":2023,"publication_date":"2023-05-11","ids":{"openalex":"https://openalex.org/W4376142003","doi":"https://doi.org/10.1080/00036811.2023.2208126"},"language":"en","primary_location":{"id":"doi:10.1080/00036811.2023.2208126","doi":"https://doi.org/10.1080/00036811.2023.2208126","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00036811.2023.2208126","pdf_url":null,"source":{"id":"https://openalex.org/S68029218","display_name":"Applicable Analysis","issn_l":"0003-6811","issn":["0003-6811","1026-7360","1563-504X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applicable Analysis","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5070859653","display_name":"Sabeur Mansouri","orcid":"https://orcid.org/0000-0002-4785-0585","observed_orcids":["https://orcid.org/0000-0002-4785-0585"]},"institutions":[{"id":"https://openalex.org/I166928557","display_name":"University of Monastir","ror":"https://ror.org/00nhtcg76","country_code":"TN","type":"education","lineage":["https://openalex.org/I166928557"]}],"countries":["TN"],"is_corresponding":true,"raw_author_name":"Sabeur Mansouri","raw_affiliation_strings":["LR Analysis and Control of PDEs, LR 22ES03, Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir, Monastir, Tunisia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LR Analysis and Control of PDEs, LR 22ES03, Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir, Monastir, Tunisia","institution_ids":["https://openalex.org/I166928557"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5117576869","display_name":"Mohamed Hocine Braiki","orcid":"https://orcid.org/0009-0003-2104-7908","observed_orcids":["https://orcid.org/0009-0003-2104-7908"]},"institutions":[{"id":"https://openalex.org/I4210124230","display_name":"Universit\u00e9 Mustapha Stambouli de Mascara","ror":"https://ror.org/02vqddp65","country_code":"DZ","type":"education","lineage":["https://openalex.org/I4210124230"]},{"id":"https://openalex.org/I4210125514","display_name":"Universit\u00e9 Djilali de Sidi Bel Abb\u00e8s","ror":"https://ror.org/0378szg41","country_code":"DZ","type":"education","lineage":["https://openalex.org/I4210125514"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Hocine Mohamed Braiki","raw_affiliation_strings":["Department of Mathematics, Faculty of axact sciences, Mustapha Stambouli University, Mascara, Algeria","Laboratory of Analysis and Control of Partial Differential Equations, Djillali Liabes University, Sidi Bel Abbes, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of axact sciences, Mustapha Stambouli University, Mascara, Algeria","institution_ids":["https://openalex.org/I4210124230"]},{"raw_affiliation_string":"Laboratory of Analysis and Control of Partial Differential Equations, Djillali Liabes University, Sidi Bel Abbes, Algeria","institution_ids":["https://openalex.org/I4210125514"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091469559","display_name":"Mama Abdelli","orcid":"https://orcid.org/0000-0003-2641-5223","observed_orcids":["https://orcid.org/0000-0003-2641-5223"]},"institutions":[{"id":"https://openalex.org/I4210125514","display_name":"Universit\u00e9 Djilali de Sidi Bel Abb\u00e8s","ror":"https://ror.org/0378szg41","country_code":"DZ","type":"education","lineage":["https://openalex.org/I4210125514"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Mama Abdelli","raw_affiliation_strings":["Laboratory of Analysis and Control of Partial Differential Equations, Djillali Liabes University, Sidi Bel Abbes, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Analysis and Control of Partial Differential Equations, Djillali Liabes University, Sidi Bel Abbes, Algeria","institution_ids":["https://openalex.org/I4210125514"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5070859653"],"corresponding_institution_ids":["https://openalex.org/I166928557"],"apc_list":null,"apc_paid":null,"fwci":0.2617,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.41712035,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"103","issue":"4","first_page":"748","last_page":"762"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":1.0,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.0,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/kirchhoff-equations","display_name":"Kirchhoff equations","score":0.8989999890327454},{"id":"https://openalex.org/keywords/heat-equation","display_name":"heat equation","score":0.9980000257492065},{"id":"https://openalex.org/keywords/coupled-systems","display_name":"coupled systems","score":0.8370000123977661},{"id":"https://openalex.org/keywords/well-posedness","display_name":"well-posedness","score":0.949999988079071},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"exponential stability","score":0.9980000257492065},{"id":"https://openalex.org/keywords/asymptotic-behavior","display_name":"asymptotic behavior","score":0.9810000061988831},{"id":"https://openalex.org/keywords/energy-method","display_name":"energy method","score":0.972000002861023},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"augmented Lagrangian method","score":0.7379999756813049},{"id":"https://openalex.org/keywords/bounded-domains","display_name":"bounded domains","score":0.6539999842643738}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8237423896789551},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.743843138217926},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.7217008471488953},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.7163106799125671},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.595180094242096},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.5766076445579529},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5683212876319885},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.5235878229141235},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.425438791513443},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.4251530170440674},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.4248267412185669},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4196700155735016},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3905664086341858},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.22457650303840637},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06591814756393433},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","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/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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00036811.2023.2208126","doi":"https://doi.org/10.1080/00036811.2023.2208126","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00036811.2023.2208126","pdf_url":null,"source":{"id":"https://openalex.org/S68029218","display_name":"Applicable Analysis","issn_l":"0003-6811","issn":["0003-6811","1026-7360","1563-504X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applicable Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1993445569","https://openalex.org/W1999687987","https://openalex.org/W2020899673","https://openalex.org/W2049510063","https://openalex.org/W3009213622","https://openalex.org/W3113552440","https://openalex.org/W3188484024","https://openalex.org/W4388111130"],"related_works":["https://openalex.org/W3111693930","https://openalex.org/W3115644316","https://openalex.org/W3188484024","https://openalex.org/W3135436787","https://openalex.org/W4232967873","https://openalex.org/W4410454483","https://openalex.org/W4205360021","https://openalex.org/W4388111130","https://openalex.org/W4393207353","https://openalex.org/W2910043050"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,28,44],"consecrated":[3],"to":[4,46,54],"the":[5,14,26,36,41,48,52,55],"asymptotic":[6],"behavior":[7],"of":[8,13,51],"a":[9,20,32],"coupled":[10],"system":[11],"consisting":[12],"Kirchhoff":[15],"and":[16],"heat":[17],"equations":[18],"in":[19],"bounded":[21],"domain.":[22],"We":[23],"establish":[24],"that":[25],"problem":[27],"well-posed":[29],"by":[30],"using":[31],"Faedo\u2013Galerkin":[33],"scheme.":[34],"Furthermore,":[35],"energy":[37],"method":[38],"combined":[39],"with":[40],"multiplier":[42],"techniques":[43],"used":[45],"show":[47],"exponential":[49],"stability":[50],"solutions":[53],"system.":[56]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2}],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2023-05-12T00:00:00"}