{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T03:34:58Z","timestamp":1772336098089,"version":"3.50.1"},"reference-count":41,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","award":["201906230072"],"award-info":[{"award-number":["201906230072"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971308"],"award-info":[{"award-number":["11971308"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11631008"],"award-info":[{"award-number":["11631008"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Math. Anal."],"published-print":{"date-parts":[[2022,10]]},"DOI":"10.1137\/21m146733x","type":"journal-article","created":{"date-parts":[[2022,9,13]],"date-time":"2022-09-13T15:11:56Z","timestamp":1663081916000},"page":"5223-5267","source":"Crossref","is-referenced-by-count":3,"title":["On Admissible Positions of Transonic Shocks for Steady Isothermal Euler Flows in a Horizontal Flat Nozzle under Vertical Gravity"],"prefix":"10.1137","volume":"54","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7226-9266","authenticated-orcid":true,"given":"Beixiang","family":"Fang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin","family":"Gao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"351","published-online":{"date-parts":[[2022,9,13]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-011-0424-0"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/j.matpur.2007.04.008"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2006.04.015"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-03-00422-3"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3042"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-006-0025-5"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-04-03698-0"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-08-04493-0"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-009-0811-7"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1137\/080735916"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-007-0079-z"},{"key":"atypb12","volume-title":"Supersonic Flow and Shock Waves","author":"Courant R.","year":"1948"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1137\/0905002"},{"key":"atypb14","volume-title":"Grad. Stud. Math. 19","author":"Evans L. C.","year":"1998"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2021.04.007"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-012-0576-6"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.21966"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61798-0"},{"key":"atypb19","volume-title":"Pitman","author":"Grisvard P.","year":"1985"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-009-0870-9"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.4310\/MRL.2009.v16.n5.a3"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2009.09.017"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.2010.247.109"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.2011.254.129"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-012-0580-x"},{"key":"atypb26","volume-title":"Boundary Value Problems for Quasilinear Hyperbolic Systems","author":"Li T.-T.","year":"1985"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1137\/080740179"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2016.01.002"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1007\/BF00251521"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1007\/BF01976043"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1016\/j.matpur.2012.09.006"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2020.06.016"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-021-01618-7"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1137\/20M1318869"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-009-0251-8"},{"key":"atypb36","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.20025"},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2008.04.010"},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.2008.236.139"},{"key":"atypb39","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2006.10.006"},{"key":"atypb40","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2012.02.008"},{"key":"atypb41","doi-asserted-by":"publisher","DOI":"10.1007\/s10473-020-0212-8"}],"container-title":["SIAM Journal on Mathematical Analysis"],"original-title":[],"language":"en","deposited":{"date-parts":[[2022,11,1]],"date-time":"2022-11-01T02:50:58Z","timestamp":1667271058000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/21M146733X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,13]]},"references-count":41,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2022,10]]}},"alternative-id":["10.1137\/21M146733X"],"URL":"https:\/\/doi.org\/10.1137\/21m146733x","relation":{},"ISSN":["0036-1410","1095-7154"],"issn-type":[{"value":"0036-1410","type":"print"},{"value":"1095-7154","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,13]]}}}