Temporal periodic solutions of non-isentropic compressible Euler equations with geometric effects

In this article, we investigate the general qusi-one-dimensional nozzle flows governed by non-isentropic compressible Euler system. First, the steady states of the subsonic and supersonic flows are analyzed. Then, the existence, stability, and uniqueness of the subsonic temporal periodic solutions a...

Full description

Saved in:
Bibliographic Details
Published inAdvances in nonlinear analysis Vol. 13; no. 1; pp. 789 - 812
Main Authors Fang, Xixi, Ma, Shuyue, Yu, Huimin
Format Journal Article
LanguageEnglish
Published De Gruyter 27.11.2024
Subjects
35A01
35B10
35L50
geometric effects
non-isentropic compressible Euler equations
subsonic flow
temporal periodic solutions
Online AccessGet full text

Cover

Abstract In this article, we investigate the general qusi-one-dimensional nozzle flows governed by non-isentropic compressible Euler system. First, the steady states of the subsonic and supersonic flows are analyzed. Then, the existence, stability, and uniqueness of the subsonic temporal periodic solutions around the steady states are proved by constructing a new iterative format technically. Besides, further regularity and stability of the obtained temporal periodic solutions are obtained, too. The main difficulty in the proof is coming from derivative loss, which is caused by the diagonalization. Observing that the entropy is conserved along the second characteristic curve, we overcome this difficulty by transforming the derivative of entropy with respect to into a derivative along the direction of first or third characteristic. The results demonstrate that dissipative boundary feedback control can stabilize the non-isentropic compressible Euler equations in qusi-one-dimensional nozzles.
AbstractList In this article, we investigate the general qusi-one-dimensional nozzle flows governed by non-isentropic compressible Euler system. First, the steady states of the subsonic and supersonic flows are analyzed. Then, the existence, stability, and uniqueness of the subsonic temporal periodic solutions around the steady states are proved by constructing a new iterative format technically. Besides, further regularity and stability of the obtained temporal periodic solutions are obtained, too. The main difficulty in the proof is coming from derivative loss, which is caused by the diagonalization. Observing that the entropy is conserved along the second characteristic curve, we overcome this difficulty by transforming the derivative of entropy with respect to xx into a derivative along the direction of first or third characteristic. The results demonstrate that dissipative boundary feedback control can stabilize the non-isentropic compressible Euler equations in qusi-one-dimensional nozzles.
In this article, we investigate the general qusi-one-dimensional nozzle flows governed by non-isentropic compressible Euler system. First, the steady states of the subsonic and supersonic flows are analyzed. Then, the existence, stability, and uniqueness of the subsonic temporal periodic solutions around the steady states are proved by constructing a new iterative format technically. Besides, further regularity and stability of the obtained temporal periodic solutions are obtained, too. The main difficulty in the proof is coming from derivative loss, which is caused by the diagonalization. Observing that the entropy is conserved along the second characteristic curve, we overcome this difficulty by transforming the derivative of entropy with respect to into a derivative along the direction of first or third characteristic. The results demonstrate that dissipative boundary feedback control can stabilize the non-isentropic compressible Euler equations in qusi-one-dimensional nozzles.
In this article, we investigate the general qusi-one-dimensional nozzle flows governed by non-isentropic compressible Euler system. First, the steady states of the subsonic and supersonic flows are analyzed. Then, the existence, stability, and uniqueness of the subsonic temporal periodic solutions around the steady states are proved by constructing a new iterative format technically. Besides, further regularity and stability of the obtained temporal periodic solutions are obtained, too. The main difficulty in the proof is coming from derivative loss, which is caused by the diagonalization. Observing that the entropy is conserved along the second characteristic curve, we overcome this difficulty by transforming the derivative of entropy with respect to x x into a derivative along the direction of first or third characteristic. The results demonstrate that dissipative boundary feedback control can stabilize the non-isentropic compressible Euler equations in qusi-one-dimensional nozzles.
Author Fang, Xixi
Ma, Shuyue
Yu, Huimin
Author_xml – sequence: 1
  givenname: Xixi
  surname: Fang
  fullname: Fang, Xixi
  email: 2022010091@stu.sdnu.edu.cn
  organization: School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
– sequence: 2
  givenname: Shuyue
  surname: Ma
  fullname: Ma, Shuyue
  email: 2022020495@stu.sdnu.edu.cn
  organization: School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
– sequence: 3
  givenname: Huimin
  surname: Yu
  fullname: Yu, Huimin
  email: hmyu@sdnu.edu.cn
  organization: School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
BookMark eNp1kEtLw0AQxxep4PPsNV8gOvtqXW9S6gMKXhS8LZPNpG5Js3E3ofjt3bYiXpzLPP8_mP8Zm3ShI8auOFxzzfUN5h5LAUKVAMocsVPBDS-NhvfJn_qEXaa0hhy3ms9mcMrwlTZ9iNgWPUUfau-KFNpx8KFLRWiKzC19om6Ioc87FzZ9pJR81VKxGFuKBX2OeDjf-uGjWFHY0BDzLTUNuSFdsOMG20SXP_mcvT0sXudP5fLl8Xl-vyyd1HIoJTnUpnEzAqM4EDil0BDwRgpRA1Uo66moalTKKMKqEgAi_2T4TICbTuU5ez5w64Br20e_wfhlA3q7H4S4shgH71qyShvtMqoyXCshGwMOCZUwsqq0usXMujmwXAwpRWp-eRzsznC7N9zuDLc7w7Pi7qDYYjtQrGkVx69c2HUYY5f__k_JJZffRaqMFw
Cites_doi 10.1007/BF00916643
10.1007/s10473-019-0501-2
10.1137/19M1249436
10.1016/j.jmaa.2015.05.023
10.1002/mana.202200400
10.3934/cam.2023013
10.3934/dcdss.2024029
10.1007/BF01976043
10.1007/s00220-015-2376-y
10.1002/mma.3711
10.1007/BF02101185
10.1002/mma.6399
10.1017/S0308210500023635
10.1016/j.nonrwa.2012.08.012
10.1088/1361-6544/ab31ce
10.1515/anona-2020-0148
10.1016/j.jde.2022.12.042
10.1137/21M1415029
10.4310/CMS.2017.v15.n3.a10
10.1016/j.matpur.2019.10.010
10.1007/s10473-019-0206-6
10.1007/s10915-014-9851-z
10.1016/S0304-0208(08)70506-1
10.1016/j.nonrwa.2023.103954
10.1016/j.jde.2013.01.008
10.1016/j.matpur.2012.09.006
10.1016/j.jde.2009.11.031
10.1007/BF01418125
10.4310/CMS.2023.v21.n5.a7
ContentType Journal Article
DBID AAYXX
CITATION
DOA
DOI 10.1515/anona-2024-0049
DatabaseName CrossRef
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
DatabaseTitleList

CrossRef
Database_xml – sequence: 1
  dbid: DOA
  name: DOAJ Directory of Open Access Journals
  url: https://www.doaj.org/
  sourceTypes: Open Website
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 2191-950X
EndPage 812
ExternalDocumentID oai_doaj_org_article_4595cbdab915423f90caea4293bb548a
10_1515_anona_2024_0049
10_1515_anona_2024_0049131
GroupedDBID 0R~
0~D
4.4
AAFPC
AAFWJ
AAQCX
AASOL
AASQH
ABAOT
ABAQN
ABFKT
ABIQR
ABSOE
ABUVI
ABXMZ
ACGFS
ACXLN
ACZBO
ADGQD
ADGYE
ADJVZ
ADOZN
AEJTT
AENEX
AEQDQ
AEXIE
AFBAA
AFBDD
AFCXV
AFPKN
AFQUK
AHGSO
AIERV
AJATJ
AKXKS
ALMA_UNASSIGNED_HOLDINGS
AMVHM
BAKPI
BBCWN
CFGNV
EBS
GROUPED_DOAJ
HZ~
IY9
J9A
O9-
OK1
QD8
SA.
SLJYH
AAYXX
CITATION
ID FETCH-LOGICAL-c353t-3eca59fc7e09410e0c44a9e01f322d0eba3d62bda4494eabb200295091720c663
IEDL.DBID DOA
ISSN 2191-950X
IngestDate Wed Aug 27 01:26:18 EDT 2025
Tue Jul 01 00:37:50 EDT 2025
Thu Jul 10 10:30:53 EDT 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 1
Language English
License This work is licensed under the Creative Commons Attribution 4.0 International License.
http://creativecommons.org/licenses/by/4.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c353t-3eca59fc7e09410e0c44a9e01f322d0eba3d62bda4494eabb200295091720c663
OpenAccessLink https://doaj.org/article/4595cbdab915423f90caea4293bb548a
PageCount 26
ParticipantIDs doaj_primary_oai_doaj_org_article_4595cbdab915423f90caea4293bb548a
crossref_primary_10_1515_anona_2024_0049
walterdegruyter_journals_10_1515_anona_2024_0049131
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2024-11-27
PublicationDateYYYYMMDD 2024-11-27
PublicationDate_xml – month: 11
  year: 2024
  text: 2024-11-27
  day: 27
PublicationDecade 2020
PublicationTitle Advances in nonlinear analysis
PublicationYear 2024
Publisher De Gruyter
Publisher_xml – name: De Gruyter
References 2024112800574675659_j_anona-2024-0049_ref_011
2024112800574675659_j_anona-2024-0049_ref_033
2024112800574675659_j_anona-2024-0049_ref_010
2024112800574675659_j_anona-2024-0049_ref_032
2024112800574675659_j_anona-2024-0049_ref_013
2024112800574675659_j_anona-2024-0049_ref_012
2024112800574675659_j_anona-2024-0049_ref_031
2024112800574675659_j_anona-2024-0049_ref_030
2024112800574675659_j_anona-2024-0049_ref_008
2024112800574675659_j_anona-2024-0049_ref_007
2024112800574675659_j_anona-2024-0049_ref_029
2024112800574675659_j_anona-2024-0049_ref_009
2024112800574675659_j_anona-2024-0049_ref_004
2024112800574675659_j_anona-2024-0049_ref_026
2024112800574675659_j_anona-2024-0049_ref_003
2024112800574675659_j_anona-2024-0049_ref_025
2024112800574675659_j_anona-2024-0049_ref_006
2024112800574675659_j_anona-2024-0049_ref_028
2024112800574675659_j_anona-2024-0049_ref_005
2024112800574675659_j_anona-2024-0049_ref_027
2024112800574675659_j_anona-2024-0049_ref_022
2024112800574675659_j_anona-2024-0049_ref_021
2024112800574675659_j_anona-2024-0049_ref_002
2024112800574675659_j_anona-2024-0049_ref_024
2024112800574675659_j_anona-2024-0049_ref_001
2024112800574675659_j_anona-2024-0049_ref_023
2024112800574675659_j_anona-2024-0049_ref_020
2024112800574675659_j_anona-2024-0049_ref_019
2024112800574675659_j_anona-2024-0049_ref_018
2024112800574675659_j_anona-2024-0049_ref_015
2024112800574675659_j_anona-2024-0049_ref_014
2024112800574675659_j_anona-2024-0049_ref_017
2024112800574675659_j_anona-2024-0049_ref_016
References_xml – ident: 2024112800574675659_j_anona-2024-0049_ref_005
  doi: 10.1007/BF00916643
– ident: 2024112800574675659_j_anona-2024-0049_ref_028
  doi: 10.1007/s10473-019-0501-2
– ident: 2024112800574675659_j_anona-2024-0049_ref_002
  doi: 10.1137/19M1249436
– ident: 2024112800574675659_j_anona-2024-0049_ref_009
  doi: 10.1016/j.jmaa.2015.05.023
– ident: 2024112800574675659_j_anona-2024-0049_ref_016
  doi: 10.1002/mana.202200400
– ident: 2024112800574675659_j_anona-2024-0049_ref_010
– ident: 2024112800574675659_j_anona-2024-0049_ref_021
  doi: 10.3934/cam.2023013
– ident: 2024112800574675659_j_anona-2024-0049_ref_022
  doi: 10.3934/dcdss.2024029
– ident: 2024112800574675659_j_anona-2024-0049_ref_015
  doi: 10.1007/BF01976043
– ident: 2024112800574675659_j_anona-2024-0049_ref_007
  doi: 10.1007/s00220-015-2376-y
– ident: 2024112800574675659_j_anona-2024-0049_ref_003
  doi: 10.1002/mma.3711
– ident: 2024112800574675659_j_anona-2024-0049_ref_004
  doi: 10.1007/BF02101185
– ident: 2024112800574675659_j_anona-2024-0049_ref_020
  doi: 10.1002/mma.6399
– ident: 2024112800574675659_j_anona-2024-0049_ref_006
  doi: 10.1017/S0308210500023635
– ident: 2024112800574675659_j_anona-2024-0049_ref_017
  doi: 10.1016/j.nonrwa.2012.08.012
– ident: 2024112800574675659_j_anona-2024-0049_ref_012
  doi: 10.1088/1361-6544/ab31ce
– ident: 2024112800574675659_j_anona-2024-0049_ref_011
  doi: 10.1515/anona-2020-0148
– ident: 2024112800574675659_j_anona-2024-0049_ref_026
  doi: 10.1016/j.jde.2022.12.042
– ident: 2024112800574675659_j_anona-2024-0049_ref_024
  doi: 10.1137/21M1415029
– ident: 2024112800574675659_j_anona-2024-0049_ref_001
  doi: 10.4310/CMS.2017.v15.n3.a10
– ident: 2024112800574675659_j_anona-2024-0049_ref_025
  doi: 10.1016/j.matpur.2019.10.010
– ident: 2024112800574675659_j_anona-2024-0049_ref_032
  doi: 10.1007/s10473-019-0206-6
– ident: 2024112800574675659_j_anona-2024-0049_ref_029
  doi: 10.1007/s10915-014-9851-z
– ident: 2024112800574675659_j_anona-2024-0049_ref_023
  doi: 10.1016/S0304-0208(08)70506-1
– ident: 2024112800574675659_j_anona-2024-0049_ref_030
– ident: 2024112800574675659_j_anona-2024-0049_ref_033
  doi: 10.1016/j.nonrwa.2023.103954
– ident: 2024112800574675659_j_anona-2024-0049_ref_013
– ident: 2024112800574675659_j_anona-2024-0049_ref_018
– ident: 2024112800574675659_j_anona-2024-0049_ref_008
  doi: 10.1016/j.jde.2013.01.008
– ident: 2024112800574675659_j_anona-2024-0049_ref_027
  doi: 10.1016/j.matpur.2012.09.006
– ident: 2024112800574675659_j_anona-2024-0049_ref_019
  doi: 10.1016/j.jde.2009.11.031
– ident: 2024112800574675659_j_anona-2024-0049_ref_014
  doi: 10.1007/BF01418125
– ident: 2024112800574675659_j_anona-2024-0049_ref_031
  doi: 10.4310/CMS.2023.v21.n5.a7
SSID ssj0000851770
Score 2.4465506
Snippet In this article, we investigate the general qusi-one-dimensional nozzle flows governed by non-isentropic compressible Euler system. First, the steady states of...
SourceID doaj
crossref
walterdegruyter
SourceType Open Website
Index Database
Publisher
StartPage 789
SubjectTerms 35A01
35B10
35L50
geometric effects
non-isentropic compressible Euler equations
subsonic flow
temporal periodic solutions
Title Temporal periodic solutions of non-isentropic compressible Euler equations with geometric effects
URI https://www.degruyter.com/doi/10.1515/anona-2024-0049
https://doaj.org/article/4595cbdab915423f90caea4293bb548a
Volume 13
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LSwMxEA7Skz0Un1hf5ODBS-g-srvdo0pLEfTUQm9LHrOlUt263SL-e2ey21IF8eI1WUj4ZpKZ2Xz5wtiNl2PYiLAssbmyAndJX_TjBAQ2J36kg9wauuD89ByPJvJxGk13nvoiTlgtD1wD15NRGhltlU4x2AdhnnpGgcJdNNQas22XGmHM2ymmXmr2lZ8kXqPlgzG7p7CaVugTgRSUFX8LQ06tv806H-6E2sKsXH9WmxNRF2iGB6zTZIj8rp7ZIduDtyPW3tENPGZqXAtKLTjpFBd2bvjWhXiRc5yEmNOtorJYYh_Rxh3dVS-AD9YLKDm81xLfK04_YvkMild6Wsvwht9xwibDwfhhJJq3EoQJo7ASIRgVpblJAOs13wPPSKlS8PwcV6z1QKvQxgHiKGUqQWlN5IyUsoUk8AymHaeshZODM8Z1QtTP1OD-Q6HL131lw1hFfax2tLHQZbcb6LJlLYmRUSmBKGcO5YxQzgjlLrsnaLefkZa1a0ALZ42Fs78s3GXhD8NkzTpb_TYuutz5fwx9wfadx_i-CJJL1qrKNVxhElLpa-dvX83q3Q4
linkProvider Directory of Open Access Journals
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LT9wwEB7R5UD3gKCAurQFH3rgYm3e2RwpApb3gUXiZvkx2SItDc1mhfrvO5OECBBcuDqxPJoZe76xx58Bfno5hY2Y0hKXaydplfTlKElRUnPqxybIneULzheXyfgmOr2Nb5fg4OkuDJdVOpyWi39Vw5A6dIVd8EZZxzVAEXioKTfWZOEgkoxxh7-r-9knWE5ogFEPlvfHx9dX3VYLo4o09Vpinze6v4hJNXV_H1Yf6-PqTpZnUedoDVZbuCj2G_uuwxL--QL9ZySCG6AnDbvUTDBpceHurOj8SRS5ICHkHV8xKosH-sY15HXtq5mhOFzMsBT4t-H7ngvelRVTLO75nS0r2mKPTbg5OpwcjGX7cIK0YRxWMkSr4yy3KVLy5nvo2SjSGXp-TtPXeWh06JLAOB1FWYTaGK7UyBg6pIFnCYNsQY-Ew68gTMp1oJmlxYjjmG9G2oWJjkeU-hjrcAB7T6pTDw0_huK8grSsai0r1rJiLQ_gF6u2-42JreuGopyqdp6oKM5iS5KZjLBdEOaZZzVqCpqhMZRc6QGErwyj2kk3f29c8r_tD_XahZXx5OJcnZ9cnn2Dz7W7-L4M0u_Qq8oF_iA4Upmd1t3-Axv64Ew
linkToPdf http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1Lb9QwEB7BVkL0UJWXutCCDxy4WJvETrI-ltJleRUkWqk3y4_JqtJClnRXVf89M0mIFgQXrk6sjMYznm8m488AL5OKwkZOaUmsXJS0S6ZyWpQoabhMc59VMfAB509nxfxCv7_ML7fOwnBbZcRFs7lddwypk1iHDRfKBq4BisATR7mxoxXOtGSMO1nF6i7sFIVRegQ7x_O3Xz8PlRYGFWWZ9Lw-f5n9W0hqmft3Ye-m_Vs9iLIVdGb7sNejRXHcLe8DuIPfH8LuFofgI3DnHbnUUjBncR2vghjMSdSVICHkFZ8wauoVPeMW8rb11S9RnG6W2Aj80dF9XwsuyooF1t_4mq0g-l6Px3AxOz0_mcv-3gQZVK7WUmFwualCiZS7pQkmQWtnMEkr8t6YoHcqFpmPTmuj0XnPjRqGkUOZJYEgyBMYkXB4AMKX3AZqAu1FHMZSP3VRFS6fUubjQ8QxvPqlOrvq6DEspxWkZdtq2bKWLWt5DK9ZtcNrzGvdDtTNwvZuYnVu8kCSeUPQLlOVSYJDRzFTeU-5lRuD-mNhbO9z1__6Lpnf0_-a9QLufXkzsx_fnX14Bvdba0lTmZWHMFo3GzwiMLL2z3tr-wnYs99y
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Temporal+periodic+solutions+of+non-isentropic+compressible+Euler+equations+with+geometric+effects&rft.jtitle=Advances+in+nonlinear+analysis&rft.au=Fang+Xixi&rft.au=Ma+Shuyue&rft.au=Yu+Huimin&rft.date=2024-11-27&rft.pub=De+Gruyter&rft.eissn=2191-950X&rft.volume=13&rft.issue=1&rft.spage=789&rft.epage=812&rft_id=info:doi/10.1515%2Fanona-2024-0049&rft.externalDBID=DOA&rft.externalDocID=oai_doaj_org_article_4595cbdab915423f90caea4293bb548a
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2191-950X&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2191-950X&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2191-950X&client=summon