{"id":"https://openalex.org/W1979957260","doi":"https://doi.org/10.1155/2012/943621","title":"A Regularization of the Backward Problem for Nonlinear Parabolic Equation with Time-Dependent Coefficient","display_name":"A Regularization of the Backward Problem for Nonlinear Parabolic Equation with Time-Dependent Coefficient","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1979957260","doi":"https://doi.org/10.1155/2012/943621","mag":"1979957260"},"language":"en","primary_location":{"id":"doi:10.1155/2012/943621","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/943621","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/943621.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2012/943621.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067053185","display_name":"Pham Hoang Quan","orcid":null},"institutions":[{"id":"https://openalex.org/I47807185","display_name":"Saigon University","ror":"https://ror.org/01f1fsr30","country_code":"VN","type":"education","lineage":["https://openalex.org/I47807185"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Pham Hoang Quan","raw_affiliation_strings":["Department of Mathematics and Applications, Sai Gon University, 273 An Duong Vuong, District 5, Ho Chi Minh City, Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Applications, Sai Gon University, 273 An Duong Vuong, District 5, Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I47807185"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072866542","display_name":"Le Minh Triet","orcid":null},"institutions":[{"id":"https://openalex.org/I47807185","display_name":"Saigon University","ror":"https://ror.org/01f1fsr30","country_code":"VN","type":"education","lineage":["https://openalex.org/I47807185"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"Le Minh Triet","raw_affiliation_strings":["Department of Mathematics and Applications, Sai Gon University, 273 An Duong Vuong, District 5, Ho Chi Minh City, Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Applications, Sai Gon University, 273 An Duong Vuong, District 5, Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I47807185"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113567751","display_name":"Dang Duc Trong","orcid":null},"institutions":[{"id":"https://openalex.org/I123565023","display_name":"Vietnam National University Ho Chi Minh City","ror":"https://ror.org/00waaqh38","country_code":"VN","type":"education","lineage":["https://openalex.org/I123565023"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Dang Duc Trong","raw_affiliation_strings":["Department of Mathematics, University of Natural Science, Vietnam National University, 227 Nguyen Van Cu, District 5, Ho Chi Minh City, Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Natural Science, Vietnam National University, 227 Nguyen Van Cu, District 5, Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I123565023"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5072866542"],"corresponding_institution_ids":["https://openalex.org/I47807185"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.06384993,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"2012","issue":null,"first_page":"1","last_page":"20"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":1.0,"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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9986000061035156,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9973000288009644,"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/mathematics","display_name":"Mathematics","score":0.9066745638847351},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.7559030055999756},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5930192470550537},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5849303007125854},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5604807734489441},{"id":"https://openalex.org/keywords/well-posed-problem","display_name":"Well-posed problem","score":0.531177282333374},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4522654116153717}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9066745638847351},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.7559030055999756},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5930192470550537},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5849303007125854},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5604807734489441},{"id":"https://openalex.org/C106214006","wikidata":"https://www.wikidata.org/wiki/Q1455898","display_name":"Well-posed problem","level":2,"score":0.531177282333374},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4522654116153717},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2012/943621","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/943621","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/943621.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jijmms:943621","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2012/943621.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:76decd8afefb4f8ebb4cc324cbc785ea","is_oa":true,"landing_page_url":"https://doaj.org/article/76decd8afefb4f8ebb4cc324cbc785ea","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,"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":"International Journal of Mathematics and Mathematical Sciences, Vol 2012 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2012/943621","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/943621","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/943621.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320309617","display_name":"National Foundation for Science and Technology Development","ror":"https://ror.org/04rw64z44"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1979957260.pdf","grobid_xml":"https://content.openalex.org/works/W1979957260.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1965913016","https://openalex.org/W1997057424","https://openalex.org/W2011270618","https://openalex.org/W2033655097","https://openalex.org/W2075586231","https://openalex.org/W2075639017","https://openalex.org/W2084312350","https://openalex.org/W2110408955","https://openalex.org/W2111529167","https://openalex.org/W2128701170","https://openalex.org/W2145567370","https://openalex.org/W2149880248","https://openalex.org/W2154971263","https://openalex.org/W2189253638","https://openalex.org/W2494779131","https://openalex.org/W2564554552"],"related_works":["https://openalex.org/W1965313012","https://openalex.org/W2018624941","https://openalex.org/W2371498728","https://openalex.org/W2028308512","https://openalex.org/W2053258817","https://openalex.org/W2377307760","https://openalex.org/W333828107","https://openalex.org/W2242141263","https://openalex.org/W2358956893","https://openalex.org/W3008727760"],"abstract_inverted_index":{"We":[0,14],"study":[1],"the":[2,33,37],"backward":[3],"problem":[4,17],"with":[5],"time-dependent":[6],"coefficient":[7],"which":[8],"is":[9,43],"a":[10],"severely":[11],"ill-posed":[12],"problem.":[13],"regularize":[15],"this":[16],"by":[18],"combining":[19],"quasi-boundary":[20],"value":[21],"method":[22,25],"and":[23,26,36],"quasi-reversibility":[24],"then":[27],"obtain":[28],"sharp":[29],"error":[30],"estimate":[31],"between":[32],"exact":[34],"solution":[35],"regularized":[38],"solution.":[39],"A":[40],"numerical":[41],"experiment":[42],"given":[44],"in":[45],"order":[46],"to":[47],"illustrate":[48],"our":[49],"results.":[50]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}