{"id":"https://openalex.org/W2062944798","doi":"https://doi.org/10.2478/cmam-2009-0022","title":"An Adaptive Scheme to Handle the Phenomenon of Quenching for a Localized Semilinear Heat Equation with Neumann Boundary Conditions","display_name":"An Adaptive Scheme to Handle the Phenomenon of Quenching for a Localized Semilinear Heat Equation with Neumann Boundary Conditions","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2062944798","doi":"https://doi.org/10.2478/cmam-2009-0022","mag":"2062944798"},"language":"en","primary_location":{"id":"doi:10.2478/cmam-2009-0022","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2009-0022","pdf_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2009-0022/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"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":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2009-0022/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109175591","display_name":"TH. K. Kouakou","orcid":null},"institutions":[{"id":"https://openalex.org/I17024267","display_name":"Universit\u00e9 Nangui Abrogoua","ror":"https://ror.org/0462xwv27","country_code":"CI","type":"education","lineage":["https://openalex.org/I17024267"]}],"countries":["CI"],"is_corresponding":true,"raw_author_name":"TH. K. Kouakou","raw_affiliation_strings":["1Universit\u00e9 d'Abobo-Adjam\u00e9, UFR-SFA, D\u00e9partement de Math\u00e9matiques et Informatiques, 16 BP 372 Abidjan 16, C\u00f4te d'Ivoire"],"affiliations":[{"raw_affiliation_string":"1Universit\u00e9 d'Abobo-Adjam\u00e9, UFR-SFA, D\u00e9partement de Math\u00e9matiques et Informatiques, 16 BP 372 Abidjan 16, C\u00f4te d'Ivoire","institution_ids":["https://openalex.org/I17024267"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110121552","display_name":"TH. K. Boni","orcid":null},"institutions":[{"id":"https://openalex.org/I4210136418","display_name":"Institut National Polytechnique F\u00e9lix Houphou\u00ebt-Boigny","ror":"https://ror.org/03f915n15","country_code":"CI","type":"education","lineage":["https://openalex.org/I4210136418"]}],"countries":["CI"],"is_corresponding":false,"raw_author_name":"TH. K. Boni","raw_affiliation_strings":["2Institut National Polytechnique Houphou\u00e9t-Boigny de Yamoussoukro, BP 1093 Yamoussoukro, C\u00f4te d'Ivoire"],"affiliations":[{"raw_affiliation_string":"2Institut National Polytechnique Houphou\u00e9t-Boigny de Yamoussoukro, BP 1093 Yamoussoukro, C\u00f4te d'Ivoire","institution_ids":["https://openalex.org/I4210136418"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028372159","display_name":"R. K. Kouakou","orcid":"https://orcid.org/0000-0002-0739-3236"},"institutions":[{"id":"https://openalex.org/I17024267","display_name":"Universit\u00e9 Nangui Abrogoua","ror":"https://ror.org/0462xwv27","country_code":"CI","type":"education","lineage":["https://openalex.org/I17024267"]}],"countries":["CI"],"is_corresponding":false,"raw_author_name":"R. K. Kouakou","raw_affiliation_strings":["3Universit\u00e9 d'Abobo-Adjam\u00e9, UFR-SFA, D\u00e9partement de Math\u00e9matiques et Informatique, 01 bp 2954 Abidjan 01, C\u00f4te d'Ivoire"],"affiliations":[{"raw_affiliation_string":"3Universit\u00e9 d'Abobo-Adjam\u00e9, UFR-SFA, D\u00e9partement de Math\u00e9matiques et Informatique, 01 bp 2954 Abidjan 01, C\u00f4te d'Ivoire","institution_ids":["https://openalex.org/I17024267"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5109175591"],"corresponding_institution_ids":["https://openalex.org/I17024267"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12224368,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"9","issue":"4","first_page":"339","last_page":"353"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9988999962806702,"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":0.9988999962806702,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9919000267982483,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9898999929428101,"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/quenching","display_name":"Quenching (fluorescence)","score":0.8339866399765015},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.6264873147010803},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.619581401348114},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.6148035526275635},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5516336560249329},{"id":"https://openalex.org/keywords/heat-equation","display_name":"Heat equation","score":0.510097324848175},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5054988861083984},{"id":"https://openalex.org/keywords/von-neumann-architecture","display_name":"Von Neumann architecture","score":0.4755765497684479},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.45025718212127686},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4323224723339081},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41631340980529785},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.25566548109054565},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15878748893737793},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06358382105827332}],"concepts":[{"id":"https://openalex.org/C121745418","wikidata":"https://www.wikidata.org/wiki/Q585536","display_name":"Quenching (fluorescence)","level":3,"score":0.8339866399765015},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6264873147010803},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.619581401348114},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.6148035526275635},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5516336560249329},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.510097324848175},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5054988861083984},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.4755765497684479},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.45025718212127686},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4323224723339081},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41631340980529785},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25566548109054565},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15878748893737793},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06358382105827332},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C91881484","wikidata":"https://www.wikidata.org/wiki/Q191807","display_name":"Fluorescence","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2478/cmam-2009-0022","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2009-0022","pdf_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2009-0022/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"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":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.2478/cmam-2009-0022","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2009-0022","pdf_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2009-0022/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"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":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2062944798.pdf","grobid_xml":"https://content.openalex.org/works/W2062944798.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W185230949","https://openalex.org/W1500382468","https://openalex.org/W1540969907","https://openalex.org/W1969351158","https://openalex.org/W1975536006","https://openalex.org/W1994348916","https://openalex.org/W1999665628","https://openalex.org/W2000247006","https://openalex.org/W2007239264","https://openalex.org/W2009834199","https://openalex.org/W2050739816","https://openalex.org/W2111747432","https://openalex.org/W6813391973","https://openalex.org/W6814288372"],"related_works":["https://openalex.org/W4287549745","https://openalex.org/W3114280011","https://openalex.org/W2772186013","https://openalex.org/W2708774305","https://openalex.org/W2376640306","https://openalex.org/W2673504153","https://openalex.org/W2372567542","https://openalex.org/W4221167520","https://openalex.org/W2156278396","https://openalex.org/W4391376150"],"abstract_inverted_index":{"Abstract":[0],"Under":[1],"some":[2,54],"assumptions,":[3],"we":[4,52],"prove":[5],"that":[6,31],"the":[7,14,32,41,45],"solution":[8],"of":[9,13],"a":[10,19],"discrete":[11],"form":[12],"above":[15],"problem":[16],"quenches":[17],"in":[18,36],"finite":[20],"time":[21,35],"and":[22],"estimate":[23],"its":[24],"numerical":[25,33,55],"quenching":[26,34],"time.":[27],"We":[28],"also":[29],"show":[30],"certain":[37],"cases":[38],"converges":[39],"to":[40,49,57],"real":[42],"one":[43],"when":[44],"mesh":[46],"size":[47],"tends":[48],"zero.":[50],"Finally,":[51],"give":[53],"experiments":[56],"illustrate":[58],"our":[59],"analysis.":[60]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
