{"id":"https://openalex.org/W4231092039","doi":"https://doi.org/10.1137/17m1129477","title":"Steady Hydrodynamic Model of Semiconductors with Sonic Boundary: (II) Supersonic Doping Profile","display_name":"Steady Hydrodynamic Model of Semiconductors with Sonic Boundary: (II) Supersonic Doping Profile","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W4231092039","doi":"https://doi.org/10.1137/17m1129477"},"language":"en","primary_location":{"id":"doi:10.1137/17m1129477","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1129477","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","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/A5100379857","display_name":"Jingyu Li","orcid":"https://orcid.org/0000-0001-8400-0187"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jingyu Li","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015874198","display_name":"Ming Mei","orcid":"https://orcid.org/0000-0003-1760-3417"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ming Mei","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052762597","display_name":"Guojing Zhang","orcid":"https://orcid.org/0000-0003-2152-4105"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guojing Zhang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5090922693","display_name":"Kai\u2010Jun Zhang","orcid":"https://orcid.org/0000-0001-7699-8311"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kaijun Zhang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100379857"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3892,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.88819589,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"50","issue":"1","first_page":"718","last_page":"734"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9991999864578247,"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":0.9991999864578247,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.9983000159263611,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9887999892234802,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/supersonic-speed","display_name":"Supersonic speed","score":0.945345401763916},{"id":"https://openalex.org/keywords/transonic","display_name":"Transonic","score":0.9278499484062195},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5993793606758118},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.5335607528686523},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.531954288482666},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.48192763328552246},{"id":"https://openalex.org/keywords/doping","display_name":"Doping","score":0.43003469705581665},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.41645175218582153},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4068042039871216},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.38435325026512146},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.37924301624298096},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.3264274299144745},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.22518888115882874},{"id":"https://openalex.org/keywords/aerodynamics","display_name":"Aerodynamics","score":0.12415450811386108}],"concepts":[{"id":"https://openalex.org/C205991772","wikidata":"https://www.wikidata.org/wiki/Q221337","display_name":"Supersonic speed","level":2,"score":0.945345401763916},{"id":"https://openalex.org/C103838597","wikidata":"https://www.wikidata.org/wiki/Q1579556","display_name":"Transonic","level":3,"score":0.9278499484062195},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5993793606758118},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.5335607528686523},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.531954288482666},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.48192763328552246},{"id":"https://openalex.org/C57863236","wikidata":"https://www.wikidata.org/wiki/Q1130571","display_name":"Doping","level":2,"score":0.43003469705581665},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.41645175218582153},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4068042039871216},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.38435325026512146},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.37924301624298096},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3264274299144745},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.22518888115882874},{"id":"https://openalex.org/C13393347","wikidata":"https://www.wikidata.org/wiki/Q8424","display_name":"Aerodynamics","level":2,"score":0.12415450811386108},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/17m1129477","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1129477","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1290319599","display_name":null,"funder_award_id":"192571","funder_id":"https://openalex.org/F4320334841","funder_display_name":"Fonds de recherche du Qu\u00e9bec \u2013 Nature et technologies"},{"id":"https://openalex.org/G3566624333","display_name":null,"funder_award_id":"111065201","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G438228663","display_name":null,"funder_award_id":"RGPIN 354724-2016","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G6062321740","display_name":null,"funder_award_id":"11571066","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G916465453","display_name":null,"funder_award_id":"11371082","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320334841","display_name":"Fonds de recherche du Qu\u00e9bec \u2013 Nature et technologies","ror":"https://ror.org/00b9f9778"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1817556347","https://openalex.org/W1954789633","https://openalex.org/W1984057219","https://openalex.org/W1988678353","https://openalex.org/W1989004487","https://openalex.org/W1991960113","https://openalex.org/W1992318858","https://openalex.org/W2001693686","https://openalex.org/W2022086204","https://openalex.org/W2026671918","https://openalex.org/W2044736300","https://openalex.org/W2077544846","https://openalex.org/W2088763001","https://openalex.org/W2091723941","https://openalex.org/W2095892403","https://openalex.org/W2113523806","https://openalex.org/W2313534310","https://openalex.org/W2770033494","https://openalex.org/W3104516944","https://openalex.org/W3106376419"],"related_works":["https://openalex.org/W2761883268","https://openalex.org/W3036816309","https://openalex.org/W4245955223","https://openalex.org/W339539064","https://openalex.org/W87335793","https://openalex.org/W2298789585","https://openalex.org/W2543652715","https://openalex.org/W2389612288","https://openalex.org/W1987948745","https://openalex.org/W2931831557"],"abstract_inverted_index":{"This":[0],"is":[1,75,82,103,113,142],"the":[2,11,19,37,47,57,79,99,106,110,123,136,140],"second":[3],"part":[4],"of":[5,8,15,22,39,117,120,125],"our":[6],"series":[7],"studies":[9],"concerning":[10],"well-posedness/ill-posedness":[12],"and":[13,44,65,93,109,144],"regularity":[14],"stationary":[16],"solutions":[17,97,121],"to":[18,105],"hydrodynamic":[20],"model":[21],"semiconductors":[23],"represented":[24],"by":[25],"Euler--Poisson":[26],"equations":[27],"with":[28],"sonic":[29,107],"boundary":[30],"condition.":[31],"In":[32],"this":[33],"paper,":[34],"we":[35],"consider":[36],"case":[38,124],"a":[40,71,126],"supersonic":[41,63,72,91,100],"doping":[42,73,101,128],"profile,":[43],"prove":[45],"that":[46,135],"system":[48,58,141],"does":[49],"not":[50],"hold":[51],"any":[52,61,66,118],"interior":[53,62,90],"subsonic":[54],"solution;":[55],"furthermore,":[56],"doesn't":[59],"admit":[60],"solution":[64,68,92],"transonic":[67,96],"if":[69,98],"such":[70],"profile":[74,102,129],"small":[76,127,131],"enough":[77],"or":[78,130],"relaxation":[80,111,132],"time":[81,112,133],"small,":[83],"but":[84],"it":[85],"has":[86],"at":[87],"least":[88],"one":[89],"infinitely":[94],"many":[95],"close":[104],"line":[108],"large.":[114],"The":[115],"nonexistence":[116],"type":[119],"in":[122],"indicates":[134],"semiconductor":[137],"effect":[138],"for":[139],"remarkable":[143],"cannot":[145],"be":[146],"ignored.":[147]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}