{"id":"https://openalex.org/W4385849488","doi":"https://doi.org/10.33993/jnaat311-709","title":"Direct and indirect approximations to positive solution for a nonlinear reaction-diffusion problem. I. Direct (variational)","display_name":"Direct and indirect approximations to positive solution for a nonlinear reaction-diffusion problem. I. Direct (variational)","publication_year":2002,"publication_date":"2002-02-01","ids":{"openalex":"https://openalex.org/W4385849488","doi":"https://doi.org/10.33993/jnaat311-709"},"language":"en","primary_location":{"id":"doi:10.33993/jnaat311-709","doi":"https://doi.org/10.33993/jnaat311-709","is_oa":true,"landing_page_url":"http://dx.doi.org/10.33993/jnaat311-709","pdf_url":"https://ictp.acad.ro/jnaat/journal/article/download/2002-vol31-no1-art8/Gheorghiu-Trif-pdf","source":{"id":"https://openalex.org/S4387281813","display_name":"Journal of Numerical Analysis and Approximation Theory","issn_l":"2457-6794","issn":["2457-6794","2501-059X"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","erih-plus","jufo-1"],"host_organization":"https://openalex.org/I4405261334","host_organization_name":"Tiberiu Popoviciu Institute of Numerical Analysis","host_organization_lineage":["https://openalex.org/I4405261334"],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Analysis and Approximation Theory","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://ictp.acad.ro/jnaat/journal/article/download/2002-vol31-no1-art8/Gheorghiu-Trif-pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055960931","display_name":"C\u0103lin-Ioan Gheorghiu","orcid":"https://orcid.org/0000-0002-8512-2466","observed_orcids":["https://orcid.org/0000-0002-8512-2466"]},"institutions":[{"id":"https://openalex.org/I4405261334","display_name":"Tiberiu Popoviciu Institute of Numerical Analysis","ror":"https://ror.org/054w8cm30","country_code":"RO","type":"government","lineage":["https://openalex.org/I4405258765","https://openalex.org/I4405261334","https://openalex.org/I58077936"]},{"id":"https://openalex.org/I58077936","display_name":"Romanian Academy","ror":"https://ror.org/0561n6946","country_code":"RO","type":"archive","lineage":["https://openalex.org/I58077936"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"C\u0103lin-Ioan Gheorghiu","raw_affiliation_strings":["Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy, Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy, Romania","institution_ids":["https://openalex.org/I4405261334","https://openalex.org/I58077936"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079545522","display_name":"Damian Trif","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I3125347698","display_name":"Babe\u0219-Bolyai University","ror":"https://ror.org/02rmd1t30","country_code":"RO","type":"education","lineage":["https://openalex.org/I3125347698"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Damian Trif","raw_affiliation_strings":["\u201cBabes-Bolyai\u201d University, Cluj-Napoca, Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u201cBabes-Bolyai\u201d University, Cluj-Napoca, Romania","institution_ids":["https://openalex.org/I3125347698"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4633,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.52864044,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"31","issue":"1","first_page":"61","last_page":"69"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.5127000212669373,"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"}},"topics":[{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.5127000212669373,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.1306000053882599,"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/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.12680000066757202,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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-reaction-diffusion-equations","display_name":"nonlinear reaction-diffusion equations","score":0.8600000143051147},{"id":"https://openalex.org/keywords/positive-solutions","display_name":"positive solutions","score":0.8149999976158142},{"id":"https://openalex.org/keywords/two-point-boundary-value-problems","display_name":"two-point boundary value problems","score":0.8880000114440918},{"id":"https://openalex.org/keywords/bifurcation-from-infinity","display_name":"bifurcation from infinity","score":0.8289999961853027},{"id":"https://openalex.org/keywords/variational-methods","display_name":"variational methods","score":0.5609999895095825},{"id":"https://openalex.org/keywords/conditional-extremum","display_name":"conditional extremum","score":0.8169999718666077},{"id":"https://openalex.org/keywords/finite-element-analysis","display_name":"finite element analysis","score":0.7599999904632568}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7600886821746826},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6295833587646484},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5383784174919128},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.5294929146766663},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5197300910949707},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5006251335144043},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.47841864824295044},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.45473676919937134},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4443170428276062},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42000800371170044},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15662962198257446},{"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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.33993/jnaat311-709","doi":"https://doi.org/10.33993/jnaat311-709","is_oa":true,"landing_page_url":"http://dx.doi.org/10.33993/jnaat311-709","pdf_url":"https://ictp.acad.ro/jnaat/journal/article/download/2002-vol31-no1-art8/Gheorghiu-Trif-pdf","source":{"id":"https://openalex.org/S4387281813","display_name":"Journal of Numerical Analysis and Approximation Theory","issn_l":"2457-6794","issn":["2457-6794","2501-059X"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","erih-plus","jufo-1"],"host_organization":"https://openalex.org/I4405261334","host_organization_name":"Tiberiu Popoviciu Institute of Numerical Analysis","host_organization_lineage":["https://openalex.org/I4405261334"],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Analysis and Approximation Theory","raw_type":"journal-article"},{"id":"pmh:oai:ictp.acad.ro:article/709","doi":null,"is_oa":true,"landing_page_url":"https://ictp.acad.ro/jnaat/journal/article/view/2002-vol31-no1-art8","pdf_url":null,"source":{"id":"https://openalex.org/S4387281813","display_name":"Journal of Numerical Analysis and Approximation Theory","issn_l":"2457-6794","issn":["2457-6794","2501-059X"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","erih-plus","jufo-1"],"host_organization":"https://openalex.org/I4405261334","host_organization_name":"Tiberiu Popoviciu Institute of Numerical Analysis","host_organization_lineage":["https://openalex.org/I4405261334"],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2457-6794","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:72646b8b340a40d686ee589e1ae529d4","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/72646b8b340a40d686ee589e1ae529d4","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Numerical Analysis and Approximation Theory, Vol 31, Iss 1 (2002)","raw_type":"article"},{"id":"pmh:oai:doaj.org/article:c5a8d1b2d3514c5c89ace9fc13b6f8db","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/c5a8d1b2d3514c5c89ace9fc13b6f8db","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Numerical Analysis and Approximation Theory, Vol 31, Iss 1 (2002)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.33993/jnaat311-709","doi":"https://doi.org/10.33993/jnaat311-709","is_oa":true,"landing_page_url":"http://dx.doi.org/10.33993/jnaat311-709","pdf_url":"https://ictp.acad.ro/jnaat/journal/article/download/2002-vol31-no1-art8/Gheorghiu-Trif-pdf","source":{"id":"https://openalex.org/S4387281813","display_name":"Journal of Numerical Analysis and Approximation Theory","issn_l":"2457-6794","issn":["2457-6794","2501-059X"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","erih-plus","jufo-1"],"host_organization":"https://openalex.org/I4405261334","host_organization_name":"Tiberiu Popoviciu Institute of Numerical Analysis","host_organization_lineage":["https://openalex.org/I4405261334"],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Analysis and Approximation Theory","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4385849488.pdf","grobid_xml":"https://content.openalex.org/works/W4385849488.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1506437909","https://openalex.org/W1981288703","https://openalex.org/W1984539800","https://openalex.org/W2064728990","https://openalex.org/W2068896285","https://openalex.org/W2086321208","https://openalex.org/W2086950242","https://openalex.org/W2128905586","https://openalex.org/W2207223089","https://openalex.org/W2312518672","https://openalex.org/W2319535243","https://openalex.org/W4235672832","https://openalex.org/W4251728373","https://openalex.org/W6812090250"],"related_works":["https://openalex.org/W2408648529","https://openalex.org/W1594498213","https://openalex.org/W2032172947","https://openalex.org/W2020193120","https://openalex.org/W2151726224","https://openalex.org/W2091512304","https://openalex.org/W6987385400","https://openalex.org/W7099731964","https://openalex.org/W2350839670","https://openalex.org/W2004494904"],"abstract_inverted_index":{"We":[0,36],"consider":[1,83],"a":[2,19,26,32,103,107],"nonlinear,":[3],"second-order,":[4],"two-point":[5],"boundary":[6],"value":[7],"problem":[8,24,105],"that":[9,30,55],"models":[10],"some":[11,114],"reaction-diffusion":[12],"precesses.":[13],"When":[14],"the":[15,23,38,46,49,61,66,70,79],"reaction":[16],"term":[17],"has":[18,25],"particular":[20],"form,":[21],"\\(f(u)=u^{3}\\),":[22],"unique":[27],"positive":[28,71,97],"solution":[29,42,56,72],"satisfies":[31],"conserved":[33],"integral":[34],"condition.":[35],"study":[37],"bifurcation":[39],"of":[40,48],"this":[41,96],"with":[43],"respect":[44],"to":[45,69,89,95],"length":[47],"interval":[50],"and":[51],"it":[52,101],"turns":[53],"out":[54,113],"bifurcates":[57],"from":[58],"infinity.":[59],"In":[60,87],"first":[62],"part,":[63],"we":[64,82,99,111],"obtain":[65,90],"numerical":[67,85,93,115],"approximation":[68],"by":[73,102,117],"direct":[74],"variational":[75,104],"methods,":[76],"while":[77],"in":[78],"second":[80],"part":[81],"indirect":[84],"methods.":[86],"order":[88],"directly":[91],"accurate":[92],"approximations":[94],"solution,":[98],"characterize":[100],"involving":[106],"conditional":[108],"extremum.":[109],"Then":[110],"carry":[112],"experiments":[116],"usual":[118],"finite":[119],"elements":[120],"method.":[121]},"counts_by_year":[],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2023-08-16T00:00:00"}