{"id":"https://openalex.org/W7129456148","doi":"https://doi.org/10.1134/s0012266125100064","title":"On the Unique Solvability of Initial\u2013Boundary Value Problems for Parabolic Systems in a Plane Bounded Domain with General Boundary Conditions","display_name":"On the Unique Solvability of Initial\u2013Boundary Value Problems for Parabolic Systems in a Plane Bounded Domain with General Boundary Conditions","publication_year":2025,"publication_date":"2025-10-01","ids":{"openalex":"https://openalex.org/W7129456148","doi":"https://doi.org/10.1134/s0012266125100064"},"language":"en","primary_location":{"id":"doi:10.1134/s0012266125100064","doi":"https://doi.org/10.1134/s0012266125100064","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0012266125100064","pdf_url":null,"source":{"id":"https://openalex.org/S71958379","display_name":"Differential Equations","issn_l":"0012-2661","issn":["0012-2661","1608-3083"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Differential Equations","raw_type":"journal-article"},"volume":null,"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/A5016942790","display_name":"S. I. Sakharov","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I19880235","display_name":"Lomonosov Moscow State University","ror":"https://ror.org/010pmpe69","country_code":"RU","type":"education","lineage":["https://openalex.org/I19880235"]},{"id":"https://openalex.org/I4405268144","display_name":"Moscow Center of Fundamental and Applied Mathematics","ror":"https://ror.org/000xg7d10","country_code":"RU","type":"facility","lineage":["https://openalex.org/I4405268144"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"S. I. Sakharov","raw_affiliation_strings":["Lomonosov Moscow State University, Moscow, 119991, Russia","Moscow Center for Fundamental and Applied Mathematics, Moscow, 119991, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lomonosov Moscow State University, Moscow, 119991, Russia","institution_ids":["https://openalex.org/I19880235"]},{"raw_affiliation_string":"Moscow Center for Fundamental and Applied Mathematics, Moscow, 119991, Russia","institution_ids":["https://openalex.org/I4405268144"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5016942790"],"corresponding_institution_ids":["https://openalex.org/I19880235","https://openalex.org/I4405268144"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.58677501,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"61","issue":"10","first_page":"1550","last_page":"1564"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9994999766349792,"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":0.9994999766349792,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":9.999999747378752e-05,"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":0.0,"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/initial-boundary-value-problem","display_name":"initial-boundary value problem","score":0.9110000133514404},{"id":"https://openalex.org/keywords/parabolic-systems","display_name":"parabolic systems","score":0.9539999961853027},{"id":"https://openalex.org/keywords/dini-continuous-coefficients","display_name":"Dini continuous coefficients","score":0.9580000042915344},{"id":"https://openalex.org/keywords/bounded-domains","display_name":"bounded domains","score":0.5979999899864197},{"id":"https://openalex.org/keywords/non-smooth-boundaries","display_name":"non-smooth boundaries","score":0.8830000162124634},{"id":"https://openalex.org/keywords/cusps","display_name":"cusps","score":0.7749999761581421},{"id":"https://openalex.org/keywords/general-boundary-conditions","display_name":"general boundary conditions","score":0.9750000238418579},{"id":"https://openalex.org/keywords/existence-and-uniqueness-of-solutions","display_name":"existence and uniqueness of solutions","score":0.7570000290870667},{"id":"https://openalex.org/keywords/classical-solutions","display_name":"classical solutions","score":0.9279999732971191},{"id":"https://openalex.org/keywords/integral-representation","display_name":"integral representation","score":0.9660000205039978},{"id":"https://openalex.org/keywords/smoothness-of-solutions","display_name":"smoothness of solutions","score":0.8389999866485596}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8855000138282776},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7355999946594238},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.7073000073432922},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.6523000001907349},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.6154000163078308},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6132000088691711},{"id":"https://openalex.org/C2456702","wikidata":"https://www.wikidata.org/wiki/Q1375954","display_name":"Vector-valued function","level":2,"score":0.5631999969482422},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.5475000143051147},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.4641999900341034},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4593000113964081},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4542999863624573},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4275999963283539},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.41990000009536743},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4009000062942505},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.3815999925136566},{"id":"https://openalex.org/C42045870","wikidata":"https://www.wikidata.org/wiki/Q2992268","display_name":"Mixed boundary condition","level":3,"score":0.3653999865055084},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.33070001006126404},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.32409998774528503},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.3116999864578247},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3093999922275543},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.30300000309944153},{"id":"https://openalex.org/C154416045","wikidata":"https://www.wikidata.org/wiki/Q5500196","display_name":"Free boundary problem","level":3,"score":0.2928999960422516},{"id":"https://openalex.org/C119741493","wikidata":"https://www.wikidata.org/wiki/Q5446587","display_name":"Fictitious domain method","level":3,"score":0.2888000011444092},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C108257041","wikidata":"https://www.wikidata.org/wiki/Q748993","display_name":"Robin boundary condition","level":4,"score":0.25780001282691956}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1134/s0012266125100064","doi":"https://doi.org/10.1134/s0012266125100064","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0012266125100064","pdf_url":null,"source":{"id":"https://openalex.org/S71958379","display_name":"Differential Equations","issn_l":"0012-2661","issn":["0012-2661","1608-3083"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Differential Equations","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1988907151","https://openalex.org/W2069204622","https://openalex.org/W2324303084","https://openalex.org/W2885890956","https://openalex.org/W2994544781","https://openalex.org/W3198066794","https://openalex.org/W4210751632","https://openalex.org/W4313200271","https://openalex.org/W4385392506","https://openalex.org/W4386610637","https://openalex.org/W4392157028","https://openalex.org/W4400778175","https://openalex.org/W4407694729","https://openalex.org/W4408530456","https://openalex.org/W4413049523"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"An":[1,87],"initial\u2013boundary":[2],"value":[3],"problem":[4,61],"is":[5,90,99],"considered":[6],"for":[7,41],"an":[8],"inhomogeneous":[9],"parabolic":[10],"system":[11],"with":[12,15,25,71],"Dini-continuous":[13],"coefficients":[14],"a":[16,21],"nonzero":[17],"initial":[18],"condition":[19],"in":[20,79],"plane":[22],"bounded":[23],"domain":[24,84],"nonsmooth":[26],"lateral":[27],"boundaries":[28],"allowing":[29],"the":[30,42,45,51,56,60,63,76,80,83,93,96],"presence":[31],"of":[32,44,55,65,75,82,95],"\u201ccusps\u201d":[33],"on":[34,50],"which":[35],"general":[36],"boundary":[37],"conditions":[38],"are":[39,69,85],"given":[40],"components":[43],"sought":[46],"vector":[47,66],"function.":[48],"Theorems":[49],"existence":[52],"and":[53,92],"uniqueness":[54],"classical":[57],"solution":[58,98],"to":[59],"from":[62],"space":[64],"functions":[67],"that":[68],"continuous":[70],"their":[72],"spatial":[73],"derivatives":[74],"first":[77],"order":[78],"closure":[81],"proved.":[86],"integral":[88],"representation":[89],"given,":[91],"smoothness":[94],"obtained":[97],"investigated.":[100]},"counts_by_year":[],"updated_date":"2026-09-23T09:40:40.371523","created_date":"2026-02-18T00:00:00"}