{"id":"https://openalex.org/W1602686979","doi":"https://doi.org/10.1137/s0036141000372039","title":"The Heat Equation in<i>L<sub>q</sub></i>((0,<i>T</i>),<i>L<sub>p</sub></i>)-Spaces with Weights","display_name":"The Heat Equation in<i>L<sub>q</sub></i>((0,<i>T</i>),<i>L<sub>p</sub></i>)-Spaces with Weights","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W1602686979","doi":"https://doi.org/10.1137/s0036141000372039","mag":"1602686979"},"language":"en","primary_location":{"id":"doi:10.1137/s0036141000372039","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141000372039","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","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/A5054561472","display_name":"\u041d. \u0412. \u041a\u0440\u044b\u043b\u043e\u0432","orcid":"https://orcid.org/0000-0002-2068-0432"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"N. V. Krylov","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5054561472"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2061,"has_fulltext":false,"cited_by_count":84,"citation_normalized_percentile":{"value":0.73772229,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"32","issue":"5","first_page":"1117","last_page":"1141"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9171000123023987,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9171000123023987,"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/T13234","display_name":"advanced mathematical theories","score":0.9003000259399414,"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/mathematics","display_name":"Mathematics","score":0.8640702962875366},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.782921552658081},{"id":"https://openalex.org/keywords/heat-equation","display_name":"Heat equation","score":0.7267728447914124},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5963702201843262},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5603520274162292},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.44574087858200073},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4301190674304962},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3942018747329712}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8640702962875366},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.782921552658081},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.7267728447914124},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5963702201843262},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5603520274162292},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.44574087858200073},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4301190674304962},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3942018747329712},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"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:10.1137/s0036141000372039","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141000372039","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W821236771","https://openalex.org/W1523471994","https://openalex.org/W1584610719","https://openalex.org/W2001075987","https://openalex.org/W2019745466","https://openalex.org/W2036384162","https://openalex.org/W2110954778","https://openalex.org/W2564409047","https://openalex.org/W2586412191"],"related_works":["https://openalex.org/W306294598","https://openalex.org/W186744944","https://openalex.org/W2134966247","https://openalex.org/W4378942808","https://openalex.org/W1994655161","https://openalex.org/W939557101","https://openalex.org/W2324557373","https://openalex.org/W2042501092","https://openalex.org/W2949335106","https://openalex.org/W3160056315"],"abstract_inverted_index":{"Existence":[0],"and":[1,39],"uniqueness":[2],"theorems":[3],"are":[4],"presented":[5],"for":[6,30],"the":[7,25,31],"heat":[8],"equation":[9],"in":[10],"Lp":[11],"spaces":[12],"with":[13,35],"or":[14],"without":[15],"weights":[16],"allowing":[17],"derivatives":[18],"of":[19,33],"solutions":[20],"to":[21,37,42],"blow":[22],"up":[23],"near":[24],"boundary.":[26],"It":[27],"is":[28],"allowed":[29],"powers":[32],"summability":[34],"respect":[36],"space":[38],"time":[40],"variables":[41],"be":[43],"different.":[44]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
