{"id":"https://openalex.org/W2018102041","doi":"https://doi.org/10.1155/2014/928148","title":"Nonexistence of Global Solutions to the Initial Boundary Value Problem for the Singularly Perturbed Sixth-Order Boussinesq-Type Equation","display_name":"Nonexistence of Global Solutions to the Initial Boundary Value Problem for the Singularly Perturbed Sixth-Order Boussinesq-Type Equation","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2018102041","doi":"https://doi.org/10.1155/2014/928148","mag":"2018102041"},"language":"en","primary_location":{"id":"doi:10.1155/2014/928148","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/928148","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/928148.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2014/928148.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102986699","display_name":"Changming Song","orcid":"https://orcid.org/0009-0003-6291-6890"},"institutions":[{"id":"https://openalex.org/I132586189","display_name":"Zhongyuan University of Technology","ror":"https://ror.org/0360zcg91","country_code":"CN","type":"education","lineage":["https://openalex.org/I132586189"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Changming Song","raw_affiliation_strings":["College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China","institution_ids":["https://openalex.org/I132586189"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101621552","display_name":"Li Ji-Na","orcid":"https://orcid.org/0000-0002-6637-609X"},"institutions":[{"id":"https://openalex.org/I132586189","display_name":"Zhongyuan University of Technology","ror":"https://ror.org/0360zcg91","country_code":"CN","type":"education","lineage":["https://openalex.org/I132586189"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jina Li","raw_affiliation_strings":["College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China","institution_ids":["https://openalex.org/I132586189"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101599164","display_name":"Ran Gao","orcid":"https://orcid.org/0000-0002-3151-7040"},"institutions":[{"id":"https://openalex.org/I132586189","display_name":"Zhongyuan University of Technology","ror":"https://ror.org/0360zcg91","country_code":"CN","type":"education","lineage":["https://openalex.org/I132586189"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ran Gao","raw_affiliation_strings":["College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China","institution_ids":["https://openalex.org/I132586189"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5102986699"],"corresponding_institution_ids":["https://openalex.org/I132586189"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":1.4659,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.79924639,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"2014","issue":null,"first_page":"1","last_page":"7"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9983000159263611,"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"}},"topics":[{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9983000159263611,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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":0.9847999811172485,"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":0.6120977401733398},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.570988118648529},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5340961813926697},{"id":"https://openalex.org/keywords/surface-tension","display_name":"Surface tension","score":0.4783446490764618},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4647502303123474},{"id":"https://openalex.org/keywords/boussinesq-approximation","display_name":"Boussinesq approximation (buoyancy)","score":0.4294637441635132},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.28909623622894287},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.19856148958206177},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.09634274244308472},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.06870371103286743}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6120977401733398},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.570988118648529},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5340961813926697},{"id":"https://openalex.org/C8892853","wikidata":"https://www.wikidata.org/wiki/Q170749","display_name":"Surface tension","level":2,"score":0.4783446490764618},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4647502303123474},{"id":"https://openalex.org/C181152433","wikidata":"https://www.wikidata.org/wiki/Q895274","display_name":"Boussinesq approximation (buoyancy)","level":5,"score":0.4294637441635132},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.28909623622894287},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.19856148958206177},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.09634274244308472},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.06870371103286743},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C54791560","wikidata":"https://www.wikidata.org/wiki/Q3285020","display_name":"Natural convection","level":3,"score":0.0},{"id":"https://openalex.org/C106836276","wikidata":"https://www.wikidata.org/wiki/Q898249","display_name":"Rayleigh number","level":4,"score":0.0},{"id":"https://openalex.org/C10899652","wikidata":"https://www.wikidata.org/wiki/Q160329","display_name":"Convection","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2014/928148","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/928148","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/928148.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1412177883","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1412177883","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:928148","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2014/928148.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:02c26560e2e2423ea1b50d7943fef94e","is_oa":true,"landing_page_url":"https://doaj.org/article/02c26560e2e2423ea1b50d7943fef94e","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":"Journal of Applied Mathematics, Vol 2014 (2014)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2014/928148","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/928148","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/928148.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1443645253","display_name":null,"funder_award_id":"11271336","funder_id":"https://openalex.org/F4320322770","funder_display_name":"Foundation of Henan Educational Committee"},{"id":"https://openalex.org/G27111345","display_name":null,"funder_award_id":"102300410275","funder_id":"https://openalex.org/F4320322770","funder_display_name":"Foundation of Henan Educational Committee"},{"id":"https://openalex.org/G4532202698","display_name":null,"funder_award_id":"11326167","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5091071670","display_name":null,"funder_award_id":"122300410166","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5889325489","display_name":null,"funder_award_id":"13A110119","funder_id":"https://openalex.org/F4320322770","funder_display_name":"Foundation of Henan Educational Committee"},{"id":"https://openalex.org/G7005117564","display_name":null,"funder_award_id":"11271336","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7056082155","display_name":null,"funder_award_id":"No. 11271336","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7555679112","display_name":null,"funder_award_id":"102300410275","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8439433530","display_name":null,"funder_award_id":"122300410166","funder_id":"https://openalex.org/F4320322770","funder_display_name":"Foundation of Henan Educational Committee"},{"id":"https://openalex.org/G8590155750","display_name":null,"funder_award_id":"13A110119","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8843699465","display_name":null,"funder_award_id":"11326167","funder_id":"https://openalex.org/F4320322770","funder_display_name":"Foundation of Henan Educational Committee"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322770","display_name":"Foundation of Henan Educational Committee","ror":"https://ror.org/00xvf9d29"},{"id":"https://openalex.org/F4320323845","display_name":"Natural Science Foundation of Henan Province","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2018102041.pdf","grobid_xml":"https://content.openalex.org/works/W2018102041.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W2001148010","https://openalex.org/W2062875950","https://openalex.org/W2108516049","https://openalex.org/W2163346915","https://openalex.org/W3091814460"],"related_works":["https://openalex.org/W4244718299","https://openalex.org/W1999519644","https://openalex.org/W3163579999","https://openalex.org/W2806303950","https://openalex.org/W2030728209","https://openalex.org/W2051519054","https://openalex.org/W2488633177","https://openalex.org/W2043702156","https://openalex.org/W2352708639","https://openalex.org/W2083247966"],"abstract_inverted_index":{"We":[0],"are":[1,69],"concerned":[2],"with":[3],"the":[4,10,18,29,53,59],"singularly":[5,11,60],"perturbed":[6,12,61],"Boussinesq-type":[7,62],"equation":[8,63],"including":[9],"sixth-order":[13],"Boussinesq":[14],"equation,":[15],"which":[16],"describes":[17],"bidirectional":[19],"propagation":[20],"of":[21,31,49],"small":[22],"amplitude":[23],"and":[24,66],"long":[25],"capillary-gravity":[26],"waves":[27],"on":[28],"surface":[30],"shallow":[32],"water":[33],"for":[34,58],"bond":[35],"number":[36],"(surface":[37],"tension":[38],"parameter)":[39],"less":[40],"than":[41],"but":[42],"very":[43],"close":[44],"to":[45,52],"1/3.":[46],"The":[47],"nonexistence":[48],"global":[50],"solution":[51],"initial":[54],"boundary":[55],"value":[56],"problem":[57],"is":[64],"discussed":[65],"two":[67],"examples":[68],"given.":[70]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}