{"id":"https://openalex.org/W4408516008","doi":"https://doi.org/10.1134/s1995080224606532","title":"Three-dimensional Initial Boundary Value Problem for a Degenerate Equation of Mixed Parabolic-Hyperbolic Type","display_name":"Three-dimensional Initial Boundary Value Problem for a Degenerate Equation of Mixed Parabolic-Hyperbolic Type","publication_year":2024,"publication_date":"2024-11-01","ids":{"openalex":"https://openalex.org/W4408516008","doi":"https://doi.org/10.1134/s1995080224606532"},"language":"en","primary_location":{"id":"doi:10.1134/s1995080224606532","doi":"https://doi.org/10.1134/s1995080224606532","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s1995080224606532","pdf_url":null,"source":{"id":"https://openalex.org/S106263159","display_name":"Lobachevskii Journal of Mathematics","issn_l":"1818-9962","issn":["1818-9962","1995-0802"],"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":"Lobachevskii Journal of Mathematics","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/A5006928383","display_name":"Stanislav Nikolaevich Sidorov","orcid":"https://orcid.org/0000-0002-3603-8719","observed_orcids":["https://orcid.org/0000-0002-3603-8719"]},"institutions":[{"id":"https://openalex.org/I7901131","display_name":"Ufa State Petroleum Technological University","ror":"https://ror.org/01ae6h598","country_code":"RU","type":"education","lineage":["https://openalex.org/I7901131"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"S. N. Sidorov","raw_affiliation_strings":["Ufa State Petroleum Technological University, 450064, Ufa, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ufa State Petroleum Technological University, 450064, Ufa, Russia","institution_ids":["https://openalex.org/I7901131"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5006928383"],"corresponding_institution_ids":["https://openalex.org/I7901131"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.35052433,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"45","issue":"11","first_page":"5683","last_page":"5698"},"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":9.999999747378752e-05,"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/mixed-parabolic-hyperbolic-equation","display_name":"mixed parabolic-hyperbolic equation","score":0.8700000047683716},{"id":"https://openalex.org/keywords/initial-boundary-value-problem","display_name":"initial-boundary value problem","score":0.9539999961853027},{"id":"https://openalex.org/keywords/uniqueness-of-solutions","display_name":"uniqueness of solutions","score":0.6579999923706055},{"id":"https://openalex.org/keywords/small-denominators","display_name":"small denominators","score":0.8849999904632568},{"id":"https://openalex.org/keywords/convergence-of-series","display_name":"convergence of series","score":0.8069999814033508},{"id":"https://openalex.org/keywords/asymptotic-behavior","display_name":"asymptotic behavior","score":0.6200000047683716},{"id":"https://openalex.org/keywords/stability-of-solutions","display_name":"stability of solutions","score":0.7509999871253967},{"id":"https://openalex.org/keywords/rectangular-prism","display_name":"rectangular prism","score":0.8610000014305115}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9467025995254517},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.76746666431427},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5836048126220703},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.550504207611084},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.487954318523407},{"id":"https://openalex.org/C111615704","wikidata":"https://www.wikidata.org/wiki/Q2627459","display_name":"Hyperbolic partial differential equation","level":3,"score":0.46495378017425537},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.46344923973083496},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.435477614402771},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.27380192279815674},{"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1134/s1995080224606532","doi":"https://doi.org/10.1134/s1995080224606532","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s1995080224606532","pdf_url":null,"source":{"id":"https://openalex.org/S106263159","display_name":"Lobachevskii Journal of Mathematics","issn_l":"1818-9962","issn":["1818-9962","1995-0802"],"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":"Lobachevskii Journal of Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1987555399","https://openalex.org/W2313278888","https://openalex.org/W2596323328","https://openalex.org/W2767057013","https://openalex.org/W2908403795","https://openalex.org/W3117324600","https://openalex.org/W3198157719","https://openalex.org/W3201036201","https://openalex.org/W4214861296","https://openalex.org/W4375817210"],"related_works":["https://openalex.org/W2971099291","https://openalex.org/W3099211396","https://openalex.org/W4317210689","https://openalex.org/W2066764747","https://openalex.org/W2040259912","https://openalex.org/W2886810076","https://openalex.org/W2941405134","https://openalex.org/W1484269119","https://openalex.org/W126524403","https://openalex.org/W2009708810"],"abstract_inverted_index":{"Abstract":[0],"For":[1],"an":[2,41],"inhomogeneous":[3],"equation":[4,114],"of":[5,28,40,48,53,67,86,93,101,112],"mixed":[6],"parabolic-hyperbolic":[7],"type":[8],"with":[9,72],"power":[10],"degeneration":[11],"in":[12,90],"a":[13,29],"rectangular":[14],"parallelepiped,":[15],"the":[16,26,38,46,49,51,65,73,84,87,91,102,105,109,113],"initial":[17],"boundary":[18,106],"value":[19],"problem":[20,52],"is":[21,31,35,115],"studied.":[22],"A":[23],"criterion":[24],"for":[25,64],"uniqueness":[27],"solution":[30,34,103],"established.":[32,116],"The":[33,99],"constructed":[36,88],"as":[37],"sum":[39],"orthogonal":[42],"series.":[43],"When":[44],"justifying":[45],"convergence":[47,85],"series,":[50],"small":[54,68],"denominators":[55,69],"from":[56,70,104],"two":[57],"natural":[58],"arguments":[59],"arose.":[60],"Estimates":[61],"are":[62],"established":[63],"separation":[66],"zero":[71],"corresponding":[74],"asymptotic":[75],"behavior.":[76],"These":[77],"estimates":[78],"made":[79],"it":[80],"possible":[81],"to":[82,96],"substantiate":[83],"series":[89],"class":[92],"regular":[94],"solutions":[95],"this":[97],"equation.":[98],"stability":[100],"function":[107],"and":[108],"right":[110],"side":[111]},"counts_by_year":[],"updated_date":"2026-09-22T06:50:58.402377","created_date":"2025-10-10T00:00:00"}