{"id":"https://openalex.org/W2951637157","doi":"https://doi.org/10.1137/130949968","title":"Analytical Expansions for Parabolic Equations","display_name":"Analytical Expansions for Parabolic Equations","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2951637157","doi":"https://doi.org/10.1137/130949968","mag":"2951637157"},"language":"en","primary_location":{"id":"doi:10.1137/130949968","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130949968","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1312.3314","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029466911","display_name":"Matthew Lorig","orcid":"https://orcid.org/0000-0001-5307-3447"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Matthew Lorig","raw_affiliation_strings":["Princeton University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Princeton University","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001028268","display_name":"Stefano Pagliarani","orcid":"https://orcid.org/0000-0003-4329-7054"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stefano Pagliarani","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5002338317","display_name":"Andrea Pascucci","orcid":"https://orcid.org/0000-0001-8837-5568"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andrea Pascucci","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6664,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.76262121,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"75","issue":"2","first_page":"468","last_page":"491"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9970999956130981,"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":0.9970999956130981,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9961000084877014,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9947999715805054,"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/strapping","display_name":"Strapping","score":0.7985413074493408},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.7431020736694336},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7253381013870239},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.592348575592041},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5664300918579102},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5549182891845703},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.505511999130249},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.5021812915802002},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46355190873146057},{"id":"https://openalex.org/keywords/heat-equation","display_name":"Heat equation","score":0.4530557692050934}],"concepts":[{"id":"https://openalex.org/C2779025673","wikidata":"https://www.wikidata.org/wiki/Q1569204","display_name":"Strapping","level":2,"score":0.7985413074493408},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.7431020736694336},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7253381013870239},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.592348575592041},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5664300918579102},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5549182891845703},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.505511999130249},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.5021812915802002},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46355190873146057},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.4530557692050934},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1137/130949968","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130949968","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:arx:papers:1312.3314","is_oa":false,"landing_page_url":"http://arxiv.org/pdf/1312.3314","pdf_url":"http://arxiv.org/pdf/1312.3314","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":"preprint"},{"id":"pmh:oai:arXiv.org:1312.3314","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1312.3314","pdf_url":"https://arxiv.org/pdf/1312.3314","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"mag:2951637157","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1312.3314.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.746.7590","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.746.7590","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1312.3314.pdf","raw_type":"text"},{"id":"mag:3123055760","is_oa":false,"landing_page_url":"https://econpapers.repec.org/RePEc:arx:papers:1312.3314","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":"RePEc: Research Papers in Economics","raw_type":null},{"id":"doi:10.48550/arxiv.1312.3314","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1312.3314","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1312.3314","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1312.3314","pdf_url":"https://arxiv.org/pdf/1312.3314","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320331267","display_name":"Fondation du Risque","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2951637157.pdf","grobid_xml":"https://content.openalex.org/works/W2951637157.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1487597787","https://openalex.org/W1970765391","https://openalex.org/W1973003145","https://openalex.org/W1976805080","https://openalex.org/W1979039678","https://openalex.org/W2028094085","https://openalex.org/W2059676916","https://openalex.org/W2060588344","https://openalex.org/W2064978316","https://openalex.org/W2084044200","https://openalex.org/W2086163885","https://openalex.org/W2097147069","https://openalex.org/W2950618784","https://openalex.org/W2953010723","https://openalex.org/W2998470103","https://openalex.org/W3122163857","https://openalex.org/W3124430067","https://openalex.org/W3124880381","https://openalex.org/W3125623964"],"related_works":["https://openalex.org/W220752614","https://openalex.org/W1939793030","https://openalex.org/W2068327981","https://openalex.org/W1121120541","https://openalex.org/W2522234620","https://openalex.org/W2084823297","https://openalex.org/W2298001602","https://openalex.org/W2572266050","https://openalex.org/W2151777373","https://openalex.org/W2352901130","https://openalex.org/W2468935422","https://openalex.org/W1990090120","https://openalex.org/W1991716775","https://openalex.org/W2803435947","https://openalex.org/W2810824006","https://openalex.org/W2041281489","https://openalex.org/W2289111810","https://openalex.org/W2007527687","https://openalex.org/W3098377117","https://openalex.org/W2011711803"],"abstract_inverted_index":{"We":[0,16],"consider":[1],"the":[2,25],"Cauchy":[3],"problem":[4],"associated":[5],"with":[6],"a":[7,18,40],"general":[8],"parabolic":[9],"partial":[10],"differential":[11],"equation":[12,31],"in":[13],"$d$":[14],"dimensions.":[15],"find":[17],"family":[19],"of":[20,29],"closed-form":[21],"asymptotic":[22],"approximations":[23],"for":[24,48],"unique":[26],"classical":[27],"solution":[28],"this":[30],"as":[32,34],"well":[33],"rigorous":[35],"short-time":[36],"error":[37],"estimates.":[38],"Using":[39],"boot-strapping":[41],"technique,":[42],"we":[43],"also":[44],"provide":[45],"convergence":[46],"results":[47],"arbitrarily":[49],"large":[50],"time":[51],"intervals.":[52]},"counts_by_year":[{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-19T15:00:24.278416","created_date":"2025-10-10T00:00:00"}