{"id":"https://openalex.org/W1509233195","doi":"https://doi.org/10.23919/ecc.2003.7086577","title":"Boundary stabilization of the wave equation with variable coefficients","display_name":"Boundary stabilization of the wave equation with variable coefficients","publication_year":2003,"publication_date":"2003-09-01","ids":{"openalex":"https://openalex.org/W1509233195","doi":"https://doi.org/10.23919/ecc.2003.7086577","mag":"1509233195"},"language":"en","primary_location":{"id":"doi:10.23919/ecc.2003.7086577","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2003.7086577","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2003 European Control Conference (ECC)","raw_type":"proceedings-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/A5023713913","display_name":"Salah\u2010Eddine Rebiai","orcid":"https://orcid.org/0000-0002-0595-0094"},"institutions":[{"id":"https://openalex.org/I162489102","display_name":"University of Batna 1","ror":"https://ror.org/04hrbe508","country_code":"DZ","type":"education","lineage":["https://openalex.org/I162489102"]}],"countries":["DZ"],"is_corresponding":true,"raw_author_name":"S. E. Rebiai","raw_affiliation_strings":["Department of Mathematics, University of Batna, Batna, Algeria","Department of Mathematics, Faculty of Sciences, University of Batna, 05000 Batna, Algeria"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Batna, Batna, Algeria","institution_ids":["https://openalex.org/I162489102"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Sciences, University of Batna, 05000 Batna, Algeria","institution_ids":["https://openalex.org/I162489102"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5023713913"],"corresponding_institution_ids":["https://openalex.org/I162489102"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.03958022,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"3462","last_page":"3466"},"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":0.9997000098228455,"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":0.9997000098228455,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9933000206947327,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.96670001745224,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.6165081858634949},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5912665128707886},{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.5662417411804199},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5568980574607849},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.5477879643440247},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5183347463607788},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.5065184831619263},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4817831218242645},{"id":"https://openalex.org/keywords/principal-part","display_name":"Principal part","score":0.43093860149383545},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.320378839969635}],"concepts":[{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.6165081858634949},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5912665128707886},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.5662417411804199},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5568980574607849},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.5477879643440247},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5183347463607788},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.5065184831619263},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4817831218242645},{"id":"https://openalex.org/C194053038","wikidata":"https://www.wikidata.org/wiki/Q7245087","display_name":"Principal part","level":2,"score":0.43093860149383545},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.320378839969635},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23919/ecc.2003.7086577","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2003.7086577","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2003 European Control Conference (ECC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.550000011920929}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1969545404","https://openalex.org/W1976391307","https://openalex.org/W1995358042","https://openalex.org/W2063186913","https://openalex.org/W2310394169"],"related_works":["https://openalex.org/W2371200319","https://openalex.org/W2367609594","https://openalex.org/W2350320737","https://openalex.org/W2391455523","https://openalex.org/W2739518152","https://openalex.org/W2091416718","https://openalex.org/W2998711696","https://openalex.org/W2805583352","https://openalex.org/W2915866335","https://openalex.org/W2962978077"],"abstract_inverted_index":{"This":[0],"paper":[1],"establishes":[2],"the":[3,7,10,13,20,29],"exponential":[4],"decay":[5],"of":[6,9,12],"energy":[8],"solution":[11],"wave":[14],"equation":[15],"with":[16,40],"variable":[17],"coefficients":[18],"in":[19,28],"principal":[21],"part":[22],"subject":[23],"to":[24],"dissipative":[25],"feedback":[26],"acting":[27],"Neumann":[30],"boundary":[31],"condition.":[32],"The":[33],"approach":[34],"adopted":[35],"uses":[36],"Riemannian":[37],"geometry":[38],"combined":[39],"classical":[41],"differential":[42],"multipliers.":[43]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}