{"id":"https://openalex.org/W7220537814","doi":null,"title":"Global existence and polynomial decay for a logarithmic damped wave equation with power-type nonlinearity","display_name":"Global existence and polynomial decay for a logarithmic damped wave equation with power-type nonlinearity","publication_year":2026,"publication_date":"2026-06-02","ids":{"openalex":"https://openalex.org/W7220537814"},"language":"en","primary_location":{"id":"pmh:oai:nonlinearstudies.com:article/4276","doi":null,"is_oa":true,"landing_page_url":"https://www.nonlinearstudies.com/index.php/nonlinear/article/download/4276/2657","pdf_url":null,"source":{"id":"https://openalex.org/S2764982030","display_name":"Nonlinear studies","issn_l":"1359-8678","issn":["1359-8678","2153-4373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","jufo-1","norway-1","poland-20","russia-white-list-3"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"1359-8678","raw_type":"info:eu-repo/semantics/article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.nonlinearstudies.com/index.php/nonlinear/article/download/4276/2657","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085915151","display_name":"Mohamed Houasni","orcid":"https://orcid.org/0000-0002-1966-9201","observed_orcids":["https://orcid.org/0000-0002-1966-9201"]},"institutions":[{"id":"https://openalex.org/I4210160578","display_name":"Universit\u00e9 Djilali Bounaama Khemis Miliana","ror":"https://ror.org/05n2gzs35","country_code":"DZ","type":"education","lineage":["https://openalex.org/I4210160578"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Houasni , Mohamed","raw_affiliation_strings":["Faculty of matter sciences and computer science, Department of mathematics, University of Khemis Miliana"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of matter sciences and computer science, Department of mathematics, University of Khemis Miliana","institution_ids":["https://openalex.org/I4210160578"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004785950","display_name":"Abdelkarim Kelleche","orcid":"https://orcid.org/0000-0002-8364-4041","observed_orcids":["https://orcid.org/0000-0002-8364-4041","https://orcid.org/0000-0003-4293-2378"]},"institutions":[{"id":"https://openalex.org/I4210160578","display_name":"Universit\u00e9 Djilali Bounaama Khemis Miliana","ror":"https://ror.org/05n2gzs35","country_code":"DZ","type":"education","lineage":["https://openalex.org/I4210160578"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Abdelkarim Kelleche","raw_affiliation_strings":["Department of Mathematics, Faculty of matter sciences and computer science, University of Khemis Miliana, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of matter sciences and computer science, University of Khemis Miliana, Algeria","institution_ids":["https://openalex.org/I4210160578"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081064389","display_name":"Athmane Abdallaoui","orcid":"https://orcid.org/0000-0003-1118-0361","observed_orcids":["https://orcid.org/0000-0003-1118-0361"]},"institutions":[{"id":"https://openalex.org/I4405253935","display_name":"\u00c9cole Normale Sup\u00e9rieure de Bou Saada","ror":"https://ror.org/017kx4966","country_code":"DZ","type":"education","lineage":["https://openalex.org/I4405253935"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Athmane Abdallaoui","raw_affiliation_strings":["Laboratoire de Math\u00e9matiques et Physique Appliqu\u00e9s, Ecole Normale Sup\u00e9rieur de Bou Saada, Msila, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques et Physique Appliqu\u00e9s, Ecole Normale Sup\u00e9rieur de Bou Saada, Msila, Algeria","institution_ids":["https://openalex.org/I4405253935"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"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":0.9994999766349792,"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":0.9994999766349792,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":9.999999747378752e-05,"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"}},{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","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"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-wave-equations","display_name":"nonlinear wave equations","score":0.8579999804496765},{"id":"https://openalex.org/keywords/power-law-nonlinearity","display_name":"power nonlinearity","score":0.8019999861717224},{"id":"https://openalex.org/keywords/global-existence","display_name":"global existence","score":0.968999981880188},{"id":"https://openalex.org/keywords/polynomial-decay","display_name":"polynomial decay","score":0.796999990940094},{"id":"https://openalex.org/keywords/potential-well-method","display_name":"potential well method","score":0.8989999890327454},{"id":"https://openalex.org/keywords/initial-energy","display_name":"initial energy","score":0.7250000238418579},{"id":"https://openalex.org/keywords/independent-sets","display_name":"independent sets","score":0.652999997138977},{"id":"https://openalex.org/keywords/exponential-decay","display_name":"exponential decay","score":0.5370000004768372}],"concepts":[{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.8619999885559082},{"id":"https://openalex.org/C66908091","wikidata":"https://www.wikidata.org/wiki/Q1127660","display_name":"Damped wave","level":3,"score":0.833299994468689},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.708299994468689},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6168000102043152},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6055999994277954},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.598800003528595},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.5358999967575073},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5073999762535095},{"id":"https://openalex.org/C123987485","wikidata":"https://www.wikidata.org/wiki/Q1399446","display_name":"Logarithmic decrement","level":3,"score":0.48410001397132874},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.44850000739097595},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.420199990272522},{"id":"https://openalex.org/C180188523","wikidata":"https://www.wikidata.org/wiki/Q574576","display_name":"Exponential decay","level":2,"score":0.3179999887943268},{"id":"https://openalex.org/C2779280203","wikidata":"https://www.wikidata.org/wiki/Q17121211","display_name":"Small data","level":2,"score":0.30809998512268066},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.29330000281333923},{"id":"https://openalex.org/C2989268449","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Energy method","level":2,"score":0.28049999475479126}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:nonlinearstudies.com:article/4276","doi":null,"is_oa":true,"landing_page_url":"https://www.nonlinearstudies.com/index.php/nonlinear/article/download/4276/2657","pdf_url":null,"source":{"id":"https://openalex.org/S2764982030","display_name":"Nonlinear studies","issn_l":"1359-8678","issn":["1359-8678","2153-4373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","jufo-1","norway-1","poland-20","russia-white-list-3"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"1359-8678","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:nonlinearstudies.com:article/4276","doi":null,"is_oa":true,"landing_page_url":"https://www.nonlinearstudies.com/index.php/nonlinear/article/download/4276/2657","pdf_url":null,"source":{"id":"https://openalex.org/S2764982030","display_name":"Nonlinear studies","issn_l":"1359-8678","issn":["1359-8678","2153-4373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","jufo-1","norway-1","poland-20","russia-white-list-3"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"1359-8678","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3000142752","https://openalex.org/W7201884797","https://openalex.org/W7158973895","https://openalex.org/W2959463130","https://openalex.org/W7163124974","https://openalex.org/W2793237644","https://openalex.org/W4327673256","https://openalex.org/W2623646028","https://openalex.org/W2352422411","https://openalex.org/W7204455364"],"abstract_inverted_index":{"This":[0],"paper":[1],"examines":[2],"a":[3,14,68],"nonlinear":[4],"wave":[5,64],"equation":[6],"with":[7],"logarithmic":[8,63,77],"damping":[9],"ut":[10],"ln(1+ut2":[11],")":[12],"and":[13,36,71],"polynomial":[15,69],"source":[16,70],"u|u|p?2.":[17],"Using":[18],"the":[19,27,32,37,42,46,51,73],"potential":[20,33],"well":[21,34],"method,":[22],"we":[23],"prove":[24],"that":[25],"if":[26],"initial":[28,38],"energy":[29,52],"is":[30],"below":[31],"depth":[35],"data":[39],"lie":[40],"in":[41,55],"stable":[43],"set,":[44],"then":[45],"solution":[47],"exists":[48],"globally.":[49],"Moreover,":[50],"decays":[53],"exponentially":[54],"time.":[56],"These":[57],"findings":[58],"extend":[59],"previous":[60],"results":[61],"on":[62],"equations":[65],"by":[66],"incorporating":[67],"highlight":[72],"stabilizing":[74],"effect":[75],"of":[76],"damping.":[78]},"counts_by_year":[],"updated_date":"2026-10-07T09:51:55.459714","created_date":"2026-10-06T00:00:00"}