{"id":"https://openalex.org/W4412975437","doi":"https://doi.org/10.1090/mcom/4116","title":"Numerical reconstruction and analysis of backward semilinear subdiffusion problems","display_name":"Numerical reconstruction and analysis of backward semilinear subdiffusion problems","publication_year":2025,"publication_date":"2025-07-18","ids":{"openalex":"https://openalex.org/W4412975437","doi":"https://doi.org/10.1090/mcom/4116"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/4116","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4116","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-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/A5014450583","display_name":"Xu Wu","orcid":"https://orcid.org/0000-0002-0436-5969"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xu Wu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102021236","display_name":"Jiang Yang","orcid":"https://orcid.org/0000-0002-6431-7483"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiang Yang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5002445122","display_name":"Zhi Zhou","orcid":"https://orcid.org/0000-0002-3439-0313"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhi Zhou","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.0367,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.93369627,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"95","issue":"361","first_page":"2207","last_page":"2248"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9998000264167786,"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":0.9998000264167786,"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/T10514","display_name":"Numerical methods in engineering","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/discretization","display_name":"Discretization","score":0.8214644193649292},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8000766038894653},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.6507928371429443},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5746672749519348},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5635191798210144},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5010986328125},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.482778936624527},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.43443363904953003},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.4208524823188782},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.4200212359428406},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4111875295639038},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4107295274734497},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22496917843818665},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14742723107337952}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8214644193649292},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8000766038894653},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.6507928371429443},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5746672749519348},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5635191798210144},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5010986328125},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.482778936624527},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.43443363904953003},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.4208524823188782},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.4200212359428406},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4111875295639038},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4107295274734497},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22496917843818665},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14742723107337952},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/4116","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4116","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1701579535","display_name":null,"funder_award_id":"2019B030301001","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G3419351171","display_name":null,"funder_award_id":"RCJC20210609103819018","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G3531406864","display_name":"Discovering Time-fractional Evolution Models without Full Knowledge of the Forward Map","funder_award_id":"15303122","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G4096391588","display_name":null,"funder_award_id":"RCJC20210609103819018","funder_id":"https://openalex.org/F4320316880","funder_display_name":"Natural Science Foundation of Shenzhen City"},{"id":"https://openalex.org/G4465421413","display_name":null,"funder_award_id":"RCJC20210609103819018","funder_id":"https://openalex.org/F4320330330","funder_display_name":"Guangdong Province Key Laboratory of Computational Science"},{"id":"https://openalex.org/G4950558115","display_name":null,"funder_award_id":"15303122","funder_id":"https://openalex.org/F4320316880","funder_display_name":"Natural Science Foundation of Shenzhen City"},{"id":"https://openalex.org/G5051947540","display_name":null,"funder_award_id":"2019B030301001","funder_id":"https://openalex.org/F4320330330","funder_display_name":"Guangdong Province Key Laboratory of Computational Science"},{"id":"https://openalex.org/G6453679928","display_name":null,"funder_award_id":"2019B030301001","funder_id":"https://openalex.org/F4320316880","funder_display_name":"Natural Science Foundation of Shenzhen City"},{"id":"https://openalex.org/G6684707238","display_name":null,"funder_award_id":"15303122","funder_id":"https://openalex.org/F4320330330","funder_display_name":"Guangdong Province Key Laboratory of Computational Science"}],"funders":[{"id":"https://openalex.org/F4320316880","display_name":"Natural Science Foundation of Shenzhen City","ror":null},{"id":"https://openalex.org/F4320321592","display_name":"Research Grants Council, University Grants Committee","ror":"https://ror.org/00djwmt25"},{"id":"https://openalex.org/F4320330330","display_name":"Guangdong Province Key Laboratory of Computational Science","ror":"https://ror.org/03rtxse59"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W1976739005","https://openalex.org/W2016533177","https://openalex.org/W2018348423","https://openalex.org/W2022685032","https://openalex.org/W2041540906","https://openalex.org/W2053946502","https://openalex.org/W2063879575","https://openalex.org/W2079961897","https://openalex.org/W2111271983","https://openalex.org/W2619423951","https://openalex.org/W2887687859","https://openalex.org/W2908963768","https://openalex.org/W2921309041","https://openalex.org/W2925178800","https://openalex.org/W2933027680","https://openalex.org/W2953890883","https://openalex.org/W2964112030","https://openalex.org/W2964137115","https://openalex.org/W2971771669","https://openalex.org/W2974367856","https://openalex.org/W2977386041","https://openalex.org/W2990575151","https://openalex.org/W3013884870","https://openalex.org/W3046389005","https://openalex.org/W3094937669","https://openalex.org/W3098178380","https://openalex.org/W3100497057","https://openalex.org/W3105974935","https://openalex.org/W3106441075","https://openalex.org/W3120739032","https://openalex.org/W3134261461","https://openalex.org/W3148434010","https://openalex.org/W3174733916","https://openalex.org/W3184132380","https://openalex.org/W4205888507","https://openalex.org/W4214505126","https://openalex.org/W4221151204","https://openalex.org/W4230288887","https://openalex.org/W4234093003","https://openalex.org/W4236865815","https://openalex.org/W4286976560","https://openalex.org/W4306290584","https://openalex.org/W4313192042","https://openalex.org/W4313591967","https://openalex.org/W4321460201","https://openalex.org/W4322392022","https://openalex.org/W4372353560","https://openalex.org/W4387461792","https://openalex.org/W4391600822"],"related_works":["https://openalex.org/W4213275102","https://openalex.org/W2151138761","https://openalex.org/W1965977581","https://openalex.org/W2061980133","https://openalex.org/W2050855072","https://openalex.org/W2077506191","https://openalex.org/W2387685679","https://openalex.org/W3134728064","https://openalex.org/W2115238236","https://openalex.org/W2374214022"],"abstract_inverted_index":{"This":[0,49,113],"paper":[1],"aims":[2],"to":[3,30,131,188],"develop":[4],"and":[5,24,38,44,90,110,138,158,179,193],"analyze":[6],"a":[7,46,55,147],"numerical":[8,56],"scheme":[9,79,178],"for":[10,74,87,93,107,153,173],"solving":[11,174],"the":[12,21,28,31,36,61,66,70,83,101,117,135,139,155,163,175,190,195,198,202],"backward":[13],"problem":[14,33],"of":[15,27,41,65,100,120,197],"semilinear":[16],"subdiffusion":[17],"equations.":[18],"We":[19],"establish":[20],"existence,":[22],"uniqueness,":[23],"conditional":[25,51],"stability":[26,52,143],"solution":[29,42,122],"inverse":[32],"by":[34],"applying":[35],"smoothing":[37,118],"asymptotic":[39],"properties":[40,119],"operators":[43],"constructing":[45],"fixed-point":[47],"iteration.":[48],"derived":[50,146],"further":[53],"inspires":[54],"reconstruction":[57],"scheme.":[58],"To":[59],"address":[60],"mildly":[62],"ill-posed":[63],"nature":[64],"problem,":[67,137],"we":[68,167],"employ":[69],"quasi-boundary":[71],"value":[72],"method":[73,86],"regularization.":[75],"A":[76,96],"fully":[77,176],"discrete":[78,103,121,177],"is":[80,105],"proposed,":[81],"utilizing":[82],"finite":[84],"element":[85],"spatial":[88],"discretization":[89,159],"convolution":[91],"quadrature":[92],"temporal":[94],"discretization.":[95],"thorough":[97],"error":[98,126,149],"analysis":[99,114],"resulting":[102],"system":[104],"provided":[106,187],"both":[108],"smooth":[109],"nonsmooth":[111],"data.":[112],"relies":[115],"on":[116,162],"operators,":[123],"some":[124],"nonstandard":[125],"estimates":[127,192],"optimal":[128],"with":[129],"respect":[130],"data":[132],"regularity":[133],"in":[134,142,201],"direct":[136],"arguments":[140],"used":[141],"analysis.":[144,203],"The":[145],"priori":[148],"estimate":[150],"offers":[151],"guidance":[152],"selecting":[154],"regularization":[156],"parameter":[157],"parameters":[160],"based":[161],"noise":[164],"level.":[165],"Moreover,":[166],"propose":[168],"an":[169],"easy-to-implement":[170],"iterative":[171],"algorithm":[172],"prove":[180],"its":[181],"linear":[182],"convergence.":[183],"Numerical":[184],"examples":[185],"are":[186],"illustrate":[189],"theoretical":[191],"demonstrate":[194],"necessity":[196],"assumption":[199],"required":[200]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-08-29T07:29:34.045763","created_date":"2025-08-05T00:00:00"}
