{"id":"https://openalex.org/W3017063379","doi":"https://doi.org/10.3390/sym12040617","title":"A Boundary Value Problem for Noninsulated Magnetic Regime in a Vacuum Diode","display_name":"A Boundary Value Problem for Noninsulated Magnetic Regime in a Vacuum Diode","publication_year":2020,"publication_date":"2020-04-14","ids":{"openalex":"https://openalex.org/W3017063379","doi":"https://doi.org/10.3390/sym12040617","mag":"3017063379"},"language":"en","primary_location":{"id":"doi:10.3390/sym12040617","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12040617","pdf_url":"https://www.mdpi.com/2073-8994/12/4/617/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/12/4/617/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066856324","display_name":"Edixon Rojas","orcid":"https://orcid.org/0000-0002-8593-0463"},"institutions":[{"id":"https://openalex.org/I36243813","display_name":"Universidad Nacional de Colombia","ror":"https://ror.org/059yx9a68","country_code":"CO","type":"education","lineage":["https://openalex.org/I36243813"]}],"countries":["CO"],"is_corresponding":true,"raw_author_name":"Edixon M. Rojas","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Universidad Nacional de Colombia, sede Bogot\u00e1 2, Bogot\u00e1, Colombia"],"raw_orcid":"https://orcid.org/0000-0002-8593-0463","affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad Nacional de Colombia, sede Bogot\u00e1 2, Bogot\u00e1, Colombia","institution_ids":["https://openalex.org/I36243813"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088335118","display_name":"\u041d. \u0410. \u0421\u0438\u0434\u043e\u0440\u043e\u0432","orcid":"https://orcid.org/0000-0001-9331-1921"},"institutions":[{"id":"https://openalex.org/I93251985","display_name":"Irkutsk State University","ror":"https://ror.org/01j99nc54","country_code":"RU","type":"education","lineage":["https://openalex.org/I93251985"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Nikolai A. Sidorov","raw_affiliation_strings":["Institute of Mathamatics and Information Technologies, Irkutsk State University, Irkutsk 664003, Russia"],"raw_orcid":"https://orcid.org/0000-0001-9331-1921","affiliations":[{"raw_affiliation_string":"Institute of Mathamatics and Information Technologies, Irkutsk State University, Irkutsk 664003, Russia","institution_ids":["https://openalex.org/I93251985"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103327674","display_name":"Aleksandr Sinitsyn","orcid":null},"institutions":[{"id":"https://openalex.org/I36243813","display_name":"Universidad Nacional de Colombia","ror":"https://ror.org/059yx9a68","country_code":"CO","type":"education","lineage":["https://openalex.org/I36243813"]}],"countries":["CO"],"is_corresponding":false,"raw_author_name":"Aleksandr V. Sinitsyn","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Universidad Nacional de Colombia, sede Bogot\u00e1 2, Bogot\u00e1, Colombia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad Nacional de Colombia, sede Bogot\u00e1 2, Bogot\u00e1, Colombia","institution_ids":["https://openalex.org/I36243813"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5066856324","https://openalex.org/A5088335118"],"corresponding_institution_ids":["https://openalex.org/I36243813","https://openalex.org/I93251985"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.208,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.49902247,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"12","issue":"4","first_page":"617","last_page":"617"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9918000102043152,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9901000261306763,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.697270393371582},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.6588765382766724},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6206855773925781},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6036338806152344},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.602360188961029},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5271468162536621},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.520193338394165},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.4866977035999298},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4834769368171692},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4557878077030182},{"id":"https://openalex.org/keywords/singular-integral","display_name":"Singular integral","score":0.4544137716293335},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3625199496746063},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23328956961631775},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11357909440994263}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.697270393371582},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.6588765382766724},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6206855773925781},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6036338806152344},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.602360188961029},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5271468162536621},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.520193338394165},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.4866977035999298},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4834769368171692},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4557878077030182},{"id":"https://openalex.org/C92571104","wikidata":"https://www.wikidata.org/wiki/Q888122","display_name":"Singular integral","level":3,"score":0.4544137716293335},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3625199496746063},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23328956961631775},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11357909440994263},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym12040617","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12040617","pdf_url":"https://www.mdpi.com/2073-8994/12/4/617/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:4171b7112192484fb7b29aec4209ea05","is_oa":true,"landing_page_url":"https://doaj.org/article/4171b7112192484fb7b29aec4209ea05","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 12, Iss 4, p 617 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym12040617","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12040617","pdf_url":"https://www.mdpi.com/2073-8994/12/4/617/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3017063379.pdf","grobid_xml":"https://content.openalex.org/works/W3017063379.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1555674425","https://openalex.org/W1628655587","https://openalex.org/W1984415839","https://openalex.org/W2002225129","https://openalex.org/W2008732507","https://openalex.org/W2014733371","https://openalex.org/W2051884536","https://openalex.org/W2078909570","https://openalex.org/W2984447139","https://openalex.org/W6652524122","https://openalex.org/W6653926878"],"related_works":["https://openalex.org/W1974618468","https://openalex.org/W2545824990","https://openalex.org/W2999616507","https://openalex.org/W2008112445","https://openalex.org/W2027204516","https://openalex.org/W2114064032","https://openalex.org/W2004695515","https://openalex.org/W4392238179","https://openalex.org/W2029287765","https://openalex.org/W2043671984"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,47,64],"study":[4],"the":[5,12,27,49,69,75],"stationary":[6],"boundary":[7,50],"value":[8,51],"problem":[9,52],"derived":[10],"from":[11],"magnetic":[13],"(non)":[14],"insulated":[15],"regime":[16],"on":[17],"a":[18,45,54],"plane":[19],"diode.":[20],"Our":[21],"main":[22],"goal":[23],"is":[24,83],"to":[25,53],"prove":[26],"existence":[28,70],"of":[29,37,57,71,80,87],"non-negative":[30],"solutions":[31],"for":[32,74],"that":[33],"nonlinear":[34,59],"singular":[35,55],"system":[36,56,79],"second-order":[38],"ordinary":[39],"differential":[40],"equations.":[41],"To":[42],"attain":[43],"such":[44],"goal,":[46],"reduce":[48],"coupled":[58],"Fredholm":[60],"integral":[61,81],"equations,":[62],"then":[63],"analyze":[65],"its":[66],"solvability":[67],"through":[68],"fixed":[72],"points":[73],"related":[76],"operators.":[77],"This":[78],"equations":[82],"studied":[84],"by":[85],"means":[86],"Leray-Schauder\u2019s":[88],"topological":[89],"degree":[90],"theory.":[91]},"counts_by_year":[{"year":2022,"cited_by_count":2}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
