{"id":"https://openalex.org/W1963526322","doi":"https://doi.org/10.1137/s0036139996312168","title":"Large Time Behavior of the Solutions to a Hydrodynamic Model for Semiconductors","display_name":"Large Time Behavior of the Solutions to a Hydrodynamic Model for Semiconductors","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W1963526322","doi":"https://doi.org/10.1137/s0036139996312168","mag":"1963526322"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139996312168","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139996312168","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},"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/A5028629975","display_name":"Roberto Natalini","orcid":"https://orcid.org/0000-0002-5453-6383"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Roberto Natalini","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086456834","display_name":"Tao Luo","orcid":"https://orcid.org/0000-0002-5656-8741"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tao Luo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101898018","display_name":"Zhouping Xin","orcid":"https://orcid.org/0000-0002-7434-2404"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhouping Xin","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5028629975"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.3161,"has_fulltext":false,"cited_by_count":142,"citation_normalized_percentile":{"value":0.97790981,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"59","issue":"3","first_page":"810","last_page":"830"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9995999932289124,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.9995999932289124,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9781000018119812,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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":0.9750000238418579,"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/uniqueness","display_name":"Uniqueness","score":0.8560450077056885},{"id":"https://openalex.org/keywords/isentropic-process","display_name":"Isentropic process","score":0.6936439871788025},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.5935943126678467},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.5907803177833557},{"id":"https://openalex.org/keywords/cauchy-problem","display_name":"Cauchy problem","score":0.5628148317337036},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5548384189605713},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.5211431980133057},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5111919045448303},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.503570020198822},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.49710920453071594},{"id":"https://openalex.org/keywords/semiconductor","display_name":"Semiconductor","score":0.43463563919067383},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32385188341140747},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.31150275468826294},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.18016836047172546},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.15793144702911377},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07949122786521912}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.8560450077056885},{"id":"https://openalex.org/C172959903","wikidata":"https://www.wikidata.org/wiki/Q907271","display_name":"Isentropic process","level":2,"score":0.6936439871788025},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.5935943126678467},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.5907803177833557},{"id":"https://openalex.org/C153635880","wikidata":"https://www.wikidata.org/wiki/Q1412436","display_name":"Cauchy problem","level":3,"score":0.5628148317337036},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5548384189605713},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.5211431980133057},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5111919045448303},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.503570020198822},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.49710920453071594},{"id":"https://openalex.org/C108225325","wikidata":"https://www.wikidata.org/wiki/Q11456","display_name":"Semiconductor","level":2,"score":0.43463563919067383},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32385188341140747},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.31150275468826294},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.18016836047172546},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.15793144702911377},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07949122786521912},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036139996312168","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139996312168","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1979627717","https://openalex.org/W2009772034","https://openalex.org/W2054654300","https://openalex.org/W2091494057","https://openalex.org/W2274776367","https://openalex.org/W2313467087"],"related_works":["https://openalex.org/W2945023710","https://openalex.org/W3145661141","https://openalex.org/W1966594808","https://openalex.org/W2798248621","https://openalex.org/W2090463462","https://openalex.org/W4380876306","https://openalex.org/W1674877062","https://openalex.org/W3146573394","https://openalex.org/W2563697776","https://openalex.org/W2078366360"],"abstract_inverted_index":{"We":[0],"establish":[1],"the":[2,9,13,37,41,52,58],"global":[3],"existence":[4,45],"of":[5,40,48],"smooth":[6],"solutions":[7,34,39,50],"to":[8,36,51],"Cauchy":[10],"problem":[11],"for":[12,20,22],"one-dimensional":[14],"isentropic":[15],"Euler--Poisson":[16],"(or":[17],"hydrodynamic)":[18],"model":[19],"semiconductors":[21],"small":[23],"initial":[24],"data.":[25],"In":[26],"particular":[27],"we":[28],"show":[29],"that,":[30],"as":[31],"$t\\to\\infty$,":[32],"these":[33],"converge":[35],"stationary":[38,49],"drift-diffusion":[42,53],"equations.":[43],"The":[44],"and":[46],"uniqueness":[47],"equations":[54],"are":[55],"proved":[56],"without":[57],"smallness":[59],"assumption.":[60]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":8}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}