{"id":"https://openalex.org/W2024879105","doi":"https://doi.org/10.1155/2013/547261","title":"Well-Posedness, Blow-Up Phenomena, and Asymptotic Profile for a Weakly Dissipative Modified Two-Component Camassa-Holm Equation","display_name":"Well-Posedness, Blow-Up Phenomena, and Asymptotic Profile for a Weakly Dissipative Modified Two-Component Camassa-Holm Equation","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2024879105","doi":"https://doi.org/10.1155/2013/547261","mag":"2024879105"},"language":"en","primary_location":{"id":"doi:10.1155/2013/547261","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/547261","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/547261.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/2013/547261.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010068261","display_name":"Yongsheng Mi","orcid":null},"institutions":[{"id":"https://openalex.org/I32377083","display_name":"Yangtze Normal University","ror":"https://ror.org/05v8v7d33","country_code":"CN","type":"education","lineage":["https://openalex.org/I32377083"]},{"id":"https://openalex.org/I158842170","display_name":"Chongqing University","ror":"https://ror.org/023rhb549","country_code":"CN","type":"education","lineage":["https://openalex.org/I158842170"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yongsheng Mi","raw_affiliation_strings":["College of Mathematics and Computer Sciences, Yangtze Normal University, Chongqing, Fuling 408100, China","College of Mathematics and Statistics, Chongqing University, Chongqing 400044, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Computer Sciences, Yangtze Normal University, Chongqing, Fuling 408100, China","institution_ids":["https://openalex.org/I32377083"]},{"raw_affiliation_string":"College of Mathematics and Statistics, Chongqing University, Chongqing 400044, China","institution_ids":["https://openalex.org/I158842170"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100855415","display_name":"Chunlai Mu","orcid":null},"institutions":[{"id":"https://openalex.org/I158842170","display_name":"Chongqing University","ror":"https://ror.org/023rhb549","country_code":"CN","type":"education","lineage":["https://openalex.org/I158842170"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chunlai Mu","raw_affiliation_strings":["College of Mathematics and Statistics, Chongqing University, Chongqing 400044, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Chongqing University, Chongqing 400044, China","institution_ids":["https://openalex.org/I158842170"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5010068261"],"corresponding_institution_ids":["https://openalex.org/I158842170","https://openalex.org/I32377083"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.2492,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.56927739,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"11"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":1.0,"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/T11575","display_name":"Nonlinear Photonic Systems","score":0.9919000267982483,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9890999794006348,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/dissipative-system","display_name":"Dissipative system","score":0.8694719672203064},{"id":"https://openalex.org/keywords/camassa\u2013holm-equation","display_name":"Camassa\u2013Holm equation","score":0.7259784936904907},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.7199115753173828},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6368444561958313},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.5390595197677612},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4671667814254761},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3649534583091736},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21601009368896484},{"id":"https://openalex.org/keywords/integrable-system","display_name":"Integrable system","score":0.04952016472816467},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.048027247190475464}],"concepts":[{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.8694719672203064},{"id":"https://openalex.org/C24454023","wikidata":"https://www.wikidata.org/wiki/Q5025006","display_name":"Camassa\u2013Holm equation","level":3,"score":0.7259784936904907},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.7199115753173828},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6368444561958313},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.5390595197677612},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4671667814254761},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3649534583091736},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21601009368896484},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.04952016472816467},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.048027247190475464}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2013/547261","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/547261","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/547261.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/1394808127","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1394808127","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:547261","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2013/547261.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:dbebc4202820492196ac3c00ede5abc8","is_oa":true,"landing_page_url":"https://doaj.org/article/dbebc4202820492196ac3c00ede5abc8","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"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 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/547261","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/547261","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/547261.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/G1642978047","display_name":null,"funder_award_id":"1137138","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4530006456","display_name":null,"funder_award_id":"11371384","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4781851110","display_name":null,"funder_award_id":"cstc2013jcyjA0940","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5522227371","display_name":null,"funder_award_id":"2013ABA2036","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6507447573","display_name":null,"funder_award_id":"several","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8721184798","display_name":null,"funder_award_id":"2013ABA2036","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2024879105.pdf","grobid_xml":"https://content.openalex.org/works/W2024879105.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W1964524722","https://openalex.org/W1986910101","https://openalex.org/W1987119463","https://openalex.org/W1994929667","https://openalex.org/W1996480499","https://openalex.org/W1997469526","https://openalex.org/W2004206567","https://openalex.org/W2012496761","https://openalex.org/W2015749938","https://openalex.org/W2019136248","https://openalex.org/W2020865064","https://openalex.org/W2021769583","https://openalex.org/W2026031976","https://openalex.org/W2027632481","https://openalex.org/W2027692750","https://openalex.org/W2031955135","https://openalex.org/W2034616138","https://openalex.org/W2035605307","https://openalex.org/W2038768213","https://openalex.org/W2050784102","https://openalex.org/W2051061211","https://openalex.org/W2051214830","https://openalex.org/W2053737194","https://openalex.org/W2054744677","https://openalex.org/W2060956477","https://openalex.org/W2067052455","https://openalex.org/W2068324460","https://openalex.org/W2084217855","https://openalex.org/W2085458282","https://openalex.org/W2085469835","https://openalex.org/W2087237285","https://openalex.org/W2089551570","https://openalex.org/W2092507372","https://openalex.org/W2098801586","https://openalex.org/W2119310340","https://openalex.org/W2123087434","https://openalex.org/W2329475933","https://openalex.org/W2333666081","https://openalex.org/W3105002535"],"related_works":["https://openalex.org/W2059359133","https://openalex.org/W1980761979","https://openalex.org/W4323780166","https://openalex.org/W4389115884","https://openalex.org/W2356978642","https://openalex.org/W2358479949","https://openalex.org/W1645603469","https://openalex.org/W1437054644","https://openalex.org/W2071275834","https://openalex.org/W2065200170"],"abstract_inverted_index":{"We":[0,13],"study":[1],"the":[2,16,34,43],"Cauchy":[3],"problem":[4],"of":[5,37,46],"a":[6,23],"weakly":[7],"dissipative":[8],"modified":[9],"two-component":[10],"Camassa-Holm":[11],"equation.":[12],"firstly":[14],"establish":[15],"local":[17],"well-posedness":[18],"result.":[19],"Then":[20],"we":[21,28,41],"present":[22],"precise":[24],"blow-up":[25,31,35],"scenario.":[26],"Moreover,":[27],"obtain":[29],"several":[30],"results":[32],"and":[33],"rate":[36],"strong":[38],"solutions.":[39,47],"Finally,":[40],"consider":[42],"asymptotic":[44],"behavior":[45]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}