{"id":"https://openalex.org/W4407694246","doi":"https://doi.org/10.1186/s13661-025-02022-w","title":"Model boundary value problem for the Helmholtz equation in a nonconvex angle with periodic boundary data","display_name":"Model boundary value problem for the Helmholtz equation in a nonconvex angle with periodic boundary data","publication_year":2025,"publication_date":"2025-02-18","ids":{"openalex":"https://openalex.org/W4407694246","doi":"https://doi.org/10.1186/s13661-025-02022-w"},"language":"en","primary_location":{"id":"doi:10.1186/s13661-025-02022-w","doi":"https://doi.org/10.1186/s13661-025-02022-w","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13661-025-02022-w","pdf_url":null,"source":{"id":"https://openalex.org/S61795452","display_name":"Boundary Value Problems","issn_l":"1687-2762","issn":["1687-2762","1687-2770"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","dongbi-d","norway-1","poland-40","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Boundary Value Problems","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1186/s13661-025-02022-w","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091879210","display_name":"Anatoli Merzon","orcid":"https://orcid.org/0000-0002-2916-9884","observed_orcids":["https://orcid.org/0000-0002-2916-9884"]},"institutions":[{"id":"https://openalex.org/I173755004","display_name":"Universidad Michoacana de San Nicol\u00e1s de Hidalgo","ror":"https://ror.org/00z0kq074","country_code":"MX","type":"education","lineage":["https://openalex.org/I173755004"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"A. Merzon","raw_affiliation_strings":["Instituto de F\u00edsica y Matem\u00e1ticas, Universidad Michoacana, Morelia, Michoac\u00e1n, M\u00e9xico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de F\u00edsica y Matem\u00e1ticas, Universidad Michoacana, Morelia, Michoac\u00e1n, M\u00e9xico","institution_ids":["https://openalex.org/I173755004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044033525","display_name":"P. Zhevandrov","orcid":"https://orcid.org/0000-0001-8020-9688","observed_orcids":["https://orcid.org/0000-0001-8020-9688"]},"institutions":[{"id":"https://openalex.org/I173755004","display_name":"Universidad Michoacana de San Nicol\u00e1s de Hidalgo","ror":"https://ror.org/00z0kq074","country_code":"MX","type":"education","lineage":["https://openalex.org/I173755004"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"P. Zhevandrov","raw_affiliation_strings":["Facultad de Ciencias F\u00edsico-Matem\u00e1ticas, Universidad Michoacana, Morelia, Michoac\u00e1n, M\u00e9xico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Facultad de Ciencias F\u00edsico-Matem\u00e1ticas, Universidad Michoacana, Morelia, Michoac\u00e1n, M\u00e9xico","institution_ids":["https://openalex.org/I173755004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103264597","display_name":"M. I. Romero Rodr\u00edguez","orcid":"https://orcid.org/0000-0003-2133-6251","observed_orcids":["https://orcid.org/0000-0003-2133-6251"]},"institutions":[{"id":"https://openalex.org/I41047195","display_name":"Military University Nueva Granada","ror":"https://ror.org/05n0gsn30","country_code":"CO","type":"education","lineage":["https://openalex.org/I41047195"]}],"countries":["CO"],"is_corresponding":false,"raw_author_name":"M. I. Romero Rodr\u00edguez","raw_affiliation_strings":["Facultad de Ciencias B\u00e1sicas y Aplicadas, Universidad Militar Nueva Granada, Bogot\u00e1, Colombia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Facultad de Ciencias B\u00e1sicas y Aplicadas, Universidad Militar Nueva Granada, Bogot\u00e1, Colombia","institution_ids":["https://openalex.org/I41047195"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015209732","display_name":"J. E. De la Paz M\u00e9ndez","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I3130105584","display_name":"Universidad Aut\u00f3noma de Guerrero","ror":"https://ror.org/054tbkd46","country_code":"MX","type":"education","lineage":["https://openalex.org/I3130105584"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"J. E. De la Paz M\u00e9ndez","raw_affiliation_strings":["Facultad de Matem\u00e1ticas II, Universidad Aut\u00f3noma de Guerrero, Cd. Altamirano, Guerrero, M\u00e9xico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Facultad de Matem\u00e1ticas II, Universidad Aut\u00f3noma de Guerrero, Cd. Altamirano, Guerrero, M\u00e9xico","institution_ids":["https://openalex.org/I3130105584"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5091879210"],"corresponding_institution_ids":["https://openalex.org/I173755004"],"apc_list":{"value":1890,"currency":"USD","value_usd":1890},"apc_paid":{"value":1890,"currency":"USD","value_usd":1890},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03457256,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2025","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.989300012588501,"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":0.989300012588501,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.0024999999441206455,"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"}},{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.0020000000949949026,"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/helmholtz-equation","display_name":"Helmholtz equation","score":1.0},{"id":"https://openalex.org/keywords/exterior-angles","display_name":"exterior angles","score":0.718999981880188},{"id":"https://openalex.org/keywords/periodic-boundary-conditions","display_name":"periodic boundary conditions","score":0.7450000047683716},{"id":"https://openalex.org/keywords/dirichlet-problem","display_name":"Dirichlet problem","score":0.8650000095367432},{"id":"https://openalex.org/keywords/existence-and-uniqueness-of-solutions","display_name":"existence and uniqueness of solutions","score":0.6790000200271606},{"id":"https://openalex.org/keywords/sommerfeld-integrals","display_name":"Sommerfeld integrals","score":0.9760000109672546}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7244055867195129},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.705524742603302},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6719180941581726},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6571966409683228},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6569675803184509},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.6549781560897827},{"id":"https://openalex.org/C154416045","wikidata":"https://www.wikidata.org/wiki/Q5500196","display_name":"Free boundary problem","level":3,"score":0.4926312565803528},{"id":"https://openalex.org/C42045870","wikidata":"https://www.wikidata.org/wiki/Q2992268","display_name":"Mixed boundary condition","level":3,"score":0.4780474305152893},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4411817789077759},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.41670069098472595},{"id":"https://openalex.org/C2988329120","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary values","level":3,"score":0.41560444235801697},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34178972244262695},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.25891369581222534},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1186/s13661-025-02022-w","doi":"https://doi.org/10.1186/s13661-025-02022-w","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13661-025-02022-w","pdf_url":null,"source":{"id":"https://openalex.org/S61795452","display_name":"Boundary Value Problems","issn_l":"1687-2762","issn":["1687-2762","1687-2770"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","dongbi-d","norway-1","poland-40","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Boundary Value Problems","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:a866bc14e5f34d638e45ba31514c2bf6","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/a866bc14e5f34d638e45ba31514c2bf6","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,"listed_in":[],"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":"Boundary Value Problems, Vol 2025, Iss 1, Pp 1-44 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1186/s13661-025-02022-w","doi":"https://doi.org/10.1186/s13661-025-02022-w","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13661-025-02022-w","pdf_url":null,"source":{"id":"https://openalex.org/S61795452","display_name":"Boundary Value Problems","issn_l":"1687-2762","issn":["1687-2762","1687-2770"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","dongbi-d","norway-1","poland-40","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Boundary Value Problems","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1307408089","display_name":null,"funder_award_id":"102939","funder_id":"https://openalex.org/F4320336053","funder_display_name":"Sistema Nacional de Investigadores"},{"id":"https://openalex.org/G4802003787","display_name":null,"funder_award_id":"14536","funder_id":"https://openalex.org/F4320336053","funder_display_name":"Sistema Nacional de Investigadores"},{"id":"https://openalex.org/G5967888642","display_name":null,"funder_award_id":"21641","funder_id":"https://openalex.org/F4320336053","funder_display_name":"Sistema Nacional de Investigadores"}],"funders":[{"id":"https://openalex.org/F4320329180","display_name":"Universidad Militar Nueva Granada","ror":"https://ror.org/05n0gsn30"},{"id":"https://openalex.org/F4320336053","display_name":"Sistema Nacional de Investigadores","ror":"https://ror.org/02h3fqt03"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W259014016","https://openalex.org/W589149782","https://openalex.org/W1493050828","https://openalex.org/W1963507148","https://openalex.org/W1964485558","https://openalex.org/W1971609757","https://openalex.org/W1988818508","https://openalex.org/W2007660285","https://openalex.org/W2018427448","https://openalex.org/W2030403041","https://openalex.org/W2064772542","https://openalex.org/W2070088565","https://openalex.org/W2078256816","https://openalex.org/W2079840202","https://openalex.org/W2092256535","https://openalex.org/W2093883875","https://openalex.org/W2104965675","https://openalex.org/W2137379468","https://openalex.org/W2151057545","https://openalex.org/W2171972858","https://openalex.org/W2269833606","https://openalex.org/W2327089220","https://openalex.org/W2475456177","https://openalex.org/W2503388807","https://openalex.org/W2807256850","https://openalex.org/W4226333551","https://openalex.org/W4235974713","https://openalex.org/W4256409824","https://openalex.org/W4300004301"],"related_works":["https://openalex.org/W2393913967","https://openalex.org/W1548901099","https://openalex.org/W145877682","https://openalex.org/W139491361","https://openalex.org/W2378263446","https://openalex.org/W1586418441","https://openalex.org/W1984112382","https://openalex.org/W1967691293","https://openalex.org/W2094225854","https://openalex.org/W2381926872"],"abstract_inverted_index":{"In":[0],"the":[1,6,11,24,43,46],"present":[2],"work,":[3],"we":[4],"solve":[5],"Dirichlet":[7],"boundary":[8,20],"problem":[9],"for":[10,40],"Helmholtz":[12],"equation":[13],"in":[14,30,42,57],"an":[15,31,37],"exterior":[16],"angle":[17],"with":[18],"periodic":[19],"data.":[21],"We":[22],"prove":[23],"existence":[25],"and":[26,35,55],"uniqueness":[27],"of":[28,45,51],"solution":[29],"appropriate":[32],"functional":[33],"class":[34],"give":[36],"explicit":[38],"formula":[39],"it":[41],"form":[44],"Sommerfeld":[47],"integral.":[48],"The":[49],"method":[50],"complex":[52],"characteristics":[53],"(Komech":[54],"Merzon":[56],"Stationary":[58],"Diffraction":[59],"by":[60],"Wedges,":[61],"Lect.":[62],"Notes":[63],"Math.,":[64],"vol.":[65],"2249,":[66],"Springer,":[67],"Berlin,":[68],"2019":[69],")":[70],"is":[71],"used.":[72]},"counts_by_year":[],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2025-10-10T00:00:00"}