Well-posedness of Third Order Differential Equations in Hölder Continuous Function Spaces
In this paper, by using operator-valued ${\dot{C}}^{\unicode[STIX]{x1D6FC}}$ -Fourier multiplier results on vector-valued Hölder continuous function spaces, we give a characterization of the $C^{\unicode[STIX]{x1D6FC}}$ -well-posedness for the third order differential equations $au^{\prime \prime \p...
Saved in:
| Published in: | Canadian mathematical bulletin Vol. 62; no. 4; pp. 715 - 726 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Canada
Canadian Mathematical Society
01.12.2019
Cambridge University Press |
| Subjects: | |
| ISSN: | 0008-4395, 1496-4287 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | In this paper, by using operator-valued
${\dot{C}}^{\unicode[STIX]{x1D6FC}}$
-Fourier multiplier results on vector-valued Hölder continuous function spaces, we give a characterization of the
$C^{\unicode[STIX]{x1D6FC}}$
-well-posedness for the third order differential equations
$au^{\prime \prime \prime }(t)+u^{\prime \prime }(t)=Au(t)+Bu^{\prime }(t)+f(t)$
, (
$t\in \mathbb{R}$
), where
$A,B$
are closed linear operators on a Banach space
$X$
such that
$D(A)\subset D(B)$
,
$a\in \mathbb{C}$
and
$0<\unicode[STIX]{x1D6FC}<1$
. |
|---|---|
| AbstractList | In this paper, by using operator-valued
${\dot{C}}^{\unicode[STIX]{x1D6FC}}$
-Fourier multiplier results on vector-valued Hölder continuous function spaces, we give a characterization of the
$C^{\unicode[STIX]{x1D6FC}}$
-well-posedness for the third order differential equations
$au^{\prime \prime \prime }(t)+u^{\prime \prime }(t)=Au(t)+Bu^{\prime }(t)+f(t)$
, (
$t\in \mathbb{R}$
), where
$A,B$
are closed linear operators on a Banach space
$X$
such that
$D(A)\subset D(B)$
,
$a\in \mathbb{C}$
and
$0<\unicode[STIX]{x1D6FC}<1$
. In this paper, by using operator-valued \({\dot{C}}^{\unicode[STIX]{x1D6FC}}\)-Fourier multiplier results on vector-valued Hölder continuous function spaces, we give a characterization of the \(C^{\unicode[STIX]{x1D6FC}}\)-well-posedness for the third order differential equations \(au^{\prime \prime \prime }(t)+u^{\prime \prime }(t)=Au(t)+Bu^{\prime }(t)+f(t)\), (\(t\in \mathbb{R}\)), where \(A,B\) are closed linear operators on a Banach space \(X\) such that \(D(A)\subset D(B)\), \(a\in \mathbb{C}\) and \(0<\unicode[STIX]{x1D6FC}<1\). |
| Author | Cai, Gang Bu, Shangquan |
| Author_xml | – sequence: 1 givenname: Shangquan surname: Bu fullname: Bu, Shangquan email: sbu@math.tsinghua.edu.cn organization: Department of Mathematical Science, University of Tsinghua, Beijing 100084, China Email: sbu@math.tsinghua.edu.cn – sequence: 2 givenname: Gang surname: Cai fullname: Cai, Gang email: caigang-aaaa@163.com organization: School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China Email: caigang-aaaa@163.com |
| BookMark | eNp1kM1Kw0AUhQepYFt9AHcDrqPzm0mWUvsjFLpoRXATJskdTUln0plk4Yv5Ar6YCS24ELmLe-E751w4EzSyzgJCt5TcCyr5w5YQkgieSpr0FxHJBRpTkcaRYIkaofGAo4FfoUkIe0KokkqO0dsr1HXUuAClhRCwM3j3UfkSb3wJHj9VxoAH21a6xvNjp9vK2YAri1ffX_WgmLke2s51AS86WwwcbxtdQLhGl0bXAW7Oe4peFvPdbBWtN8vn2eM6KlictpECWTAugDBIuUlLxbhmOZCcUiFSASI2_ZSaUaW5iHMh4sQwSZliSiYS-BTdnXIb744dhDbbu87b_mXGeJIqxXkc9yp6UhXeheDBZI2vDtp_ZpRkQ4XZnwp7Dz979CH3VfkOv9H_u34AUAV0eg |
| Cites_doi | 10.1007/978-3-0348-5075-9 10.1002/mma.1576 10.1007/s11464-014-0368-4 10.1007/s002080100231 10.1007/s11856-017-1496-9 10.1016/j.jde.2006.07.018 10.1023/A:1021778428222 10.1002/mana.201200168 10.1016/j.jmaa.2005.06.031 10.1016/j.exmath.2015.07.003 10.1016/S0096-3003(00)00112-0 10.4064/sm160-1-2 10.4064/sm215-3-1 |
| ContentType | Journal Article |
| Copyright | Canadian Mathematical Society 2018 |
| Copyright_xml | – notice: Canadian Mathematical Society 2018 |
| DBID | AAYXX CITATION 3V. 7XB 8FE 8FG 8FK 8FQ 8FV ABJCF ABUWG AFKRA BENPR BGLVJ CCPQU DWQXO HCIFZ L6V M7S PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS Q9U |
| DOI | 10.4153/S0008439518000048 |
| DatabaseName | CrossRef ProQuest Central (Corporate) ProQuest Central (purchase pre-March 2016) ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) Canadian Business & Current Affairs Database Canadian Business & Current Affairs Database (Alumni) Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland ProQuest Central ProQuest Technology Collection ProQuest One ProQuest Central Korea SciTech Premium Collection ProQuest Engineering Collection Engineering Database ProQuest Central Premium ProQuest One Academic (New) ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection ProQuest Central Basic |
| DatabaseTitle | CrossRef Engineering Database Technology Collection ProQuest One Academic Middle East (New) ProQuest Central Basic ProQuest One Academic Eastern Edition ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Technology Collection ProQuest SciTech Collection ProQuest Central China ProQuest Central CBCA Complete (Alumni Edition) ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest One Academic UKI Edition ProQuest Central Korea Materials Science & Engineering Collection CBCA Complete ProQuest Central (New) ProQuest One Academic ProQuest One Academic (New) ProQuest Central (Alumni) Engineering Collection |
| DatabaseTitleList | CrossRef Engineering Database |
| Database_xml | – sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| DocumentTitleAlternate | Well-posedness of Degenerate Equations S. Bu and G. Cai |
| EISSN | 1496-4287 |
| EndPage | 726 |
| ExternalDocumentID | 10_4153_S0008439518000048 |
| GroupedDBID | --Z -~X 09C 09E 5.9 69Q 6J9 8FQ AABWE AAEED AAGFV AANRG AASVR AAUKB AAYEQ AAYJJ ABBZL ABCQX ABGDZ ABJCF ABMYL ABUWG ABXAU ABZCX ABZEH ACGFO ACIPV ACKIV ACNCT ACQFJ ACYZP ACZWT ADDNB ADGEJ ADKIL ADOCW ADOVH ADVJH AEBAK AEBPU AENCP AETEA AFKQG AFKRA AFLVW AGABE AGBYD AGJUD AGOOT AHRGI AI. AIDBO AIOIP AJCYY AJPFC ALMA_UNASSIGNED_HOLDINGS AQJOH ARZZG ATUCA AYIQA BBLKV BCGOX BENPR BESQT BGLVJ BLZWO CCPQU CCQAD CCUQV CFBFF CGQII CHEAL CJCSC DOHLZ DWQXO EBS EGQIC EJD FRP HCIFZ HF~ IH6 IOO JHPGK KCGVB KFECR L7B LW7 M7S MVM NZEOI OHT OK1 P2P PTHSS RCA RCD ROL S10 TR2 UPT VH1 WFFJZ WH7 XJT ZCG ZMEZD 0R~ AAXMD AAYXX ABUFD ABVKB ABVZP ABXHF ACDLN ADIYS AFFHD AFZFC AKMAY AMVHM CITATION PHGZM PHGZT PQGLB 3V. 7XB 8FE 8FG 8FK L6V PKEHL PQEST PQQKQ PQUKI PRINS Q9U |
| ID | FETCH-LOGICAL-c269t-7e5c234e02e93f9d723a2be0b114494e46f6f6da217a346b4468f2512727585e3 |
| IEDL.DBID | M7S |
| ISICitedReferencesCount | 1 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000496553400002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0008-4395 |
| IngestDate | Fri Jul 25 10:59:34 EDT 2025 Sat Nov 29 05:31:02 EST 2025 Wed Mar 13 05:57:56 EDT 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 4 |
| Keywords | 34K30 47D06 34G10 Ċ -Fourier multiplier degenerate differential equation 47A10 C -well-posedness Hölder continuous function space |
| Language | English |
| License | https://www.cambridge.org/core/terms |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c269t-7e5c234e02e93f9d723a2be0b114494e46f6f6da217a346b4468f2512727585e3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| PQID | 2389773366 |
| PQPubID | 4573633 |
| PageCount | 12 |
| ParticipantIDs | proquest_journals_2389773366 crossref_primary_10_4153_S0008439518000048 cambridge_journals_10_4153_S0008439518000048 |
| PublicationCentury | 2000 |
| PublicationDate | 20191200 2019-12-00 20191201 |
| PublicationDateYYYYMMDD | 2019-12-01 |
| PublicationDate_xml | – month: 12 year: 2019 text: 20191200 |
| PublicationDecade | 2010 |
| PublicationPlace | Canada |
| PublicationPlace_xml | – name: Canada – name: Montreal |
| PublicationTitle | Canadian mathematical bulletin |
| PublicationTitleAlternate | Can. Math. Bull |
| PublicationYear | 2019 |
| Publisher | Canadian Mathematical Society Cambridge University Press |
| Publisher_xml | – name: Canadian Mathematical Society – name: Cambridge University Press |
| References | Bose (S0008439518000048_r4) 2002; 126 S0008439518000048_r7 Bose (S0008439518000048_r3) 1998; 99 S0008439518000048_r6 S0008439518000048_r5 S0008439518000048_r9 S0008439518000048_r10 S0008439518000048_r12 S0008439518000048_r2 S0008439518000048_r11 S0008439518000048_r14 S0008439518000048_r1 S0008439518000048_r13 Haase (S0008439518000048_r8) 2005 |
| References_xml | – ident: S0008439518000048_r2 doi: 10.1007/978-3-0348-5075-9 – ident: S0008439518000048_r11 doi: 10.1002/mma.1576 – ident: S0008439518000048_r5 doi: 10.1007/s11464-014-0368-4 – volume-title: The Functional Calculus for Sectorial Operators year: 2005 ident: S0008439518000048_r8 – ident: S0008439518000048_r9 doi: 10.1007/s002080100231 – ident: S0008439518000048_r14 doi: 10.1007/s11856-017-1496-9 – ident: S0008439518000048_r10 doi: 10.1016/j.jde.2006.07.018 – volume: 99 start-page: 423 year: 1998 ident: S0008439518000048_r3 article-title: Exact controllability and boundary stabilization of torsional vibrations of an internally damped flexible space structure publication-title: J. Optim. Theory Appl. doi: 10.1023/A:1021778428222 – ident: S0008439518000048_r13 doi: 10.1002/mana.201200168 – ident: S0008439518000048_r7 doi: 10.1016/j.jmaa.2005.06.031 – ident: S0008439518000048_r6 doi: 10.1016/j.exmath.2015.07.003 – volume: 126 start-page: 341 year: 2002 ident: S0008439518000048_r4 article-title: Exact controllability and boundary stabilization of flexural vibrations of an internally damped flexible space structure publication-title: Appl. Math. Comput. doi: 10.1016/S0096-3003(00)00112-0 – ident: S0008439518000048_r1 doi: 10.4064/sm160-1-2 – ident: S0008439518000048_r12 doi: 10.4064/sm215-3-1 |
| SSID | ssj0017575 |
| Score | 2.1453893 |
| Snippet | In this paper, by using operator-valued
${\dot{C}}^{\unicode[STIX]{x1D6FC}}$
-Fourier multiplier results on vector-valued Hölder continuous function spaces, we... In this paper, by using operator-valued \({\dot{C}}^{\unicode[STIX]{x1D6FC}}\)-Fourier multiplier results on vector-valued Hölder continuous function spaces,... |
| SourceID | proquest crossref cambridge |
| SourceType | Aggregation Database Index Database Publisher |
| StartPage | 715 |
| SubjectTerms | Banach spaces Continuity (mathematics) Differential equations Function space Linear operators Mathematical analysis Operators (mathematics) Well posed problems |
| Title | Well-posedness of Third Order Differential Equations in Hölder Continuous Function Spaces |
| URI | https://www.cambridge.org/core/product/identifier/S0008439518000048/type/journal_article https://www.proquest.com/docview/2389773366 |
| Volume | 62 |
| WOSCitedRecordID | wos000496553400002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVPQU databaseName: Canadian Business & Current Affairs Database customDbUrl: eissn: 1496-4287 dateEnd: 20241212 omitProxy: false ssIdentifier: ssj0017575 issn: 0008-4395 databaseCode: 8FQ dateStart: 20190301 isFulltext: true titleUrlDefault: https://search.proquest.com/cbcacomplete providerName: ProQuest – providerCode: PRVPQU databaseName: Engineering Database customDbUrl: eissn: 1496-4287 dateEnd: 20241212 omitProxy: false ssIdentifier: ssj0017575 issn: 0008-4395 databaseCode: M7S dateStart: 20190301 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1496-4287 dateEnd: 20241212 omitProxy: false ssIdentifier: ssj0017575 issn: 0008-4395 databaseCode: BENPR dateStart: 20190301 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3JTsMwEB1RygEO7Ii18oETwsKJszgnxNKqF8pWRMWlcmNbVKqS0rR8Gj_AjzFO0gJC6gXlFkdRlLFn5nnG7wEcu5JxXH8B1bHnUk9IXHNBT1FfObH2uBaRMrnYRNhqiU4nuis33LKyrXLqE3NHrdLY7pGfYWjBVIXzIDgfvlGrGmWrq6WERgWqliXByVv3HmdVhNAPCwUDJigGXr-oamLI4vaEMBP2niPyNFn85Fb4HaN-u-g87jTW_vvF67BaZpzkopgiG7Cgk01YuZnRtWZb8PKsBwM6TDOtrOcjqSHt1_5IkVtLzEmuSxEVdAYDUn8ryMEz0k9I8_PDqnwTy3HVTybpJCMNDJR2nDwObbfXNjw16u2rJi1FF2jsBtGYhtqPXe5p5uqIm0iFLpduT7MeAicv8rQXGLyURCgj0co9hJPC2CQJEyGEHprvwGKSJnoXiIpd6SG-YVza8pyMjG-YIyQzjnYCZvbgdPbLu-XSybqISqyFun8stAcnU6t0hwUVx7yHD6dG-X71t0X25w8fwDImRlHRtnIIi-PRRB_BUvw-7mejGlRE474G1ct66-6hlk-5L_u72I4 |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1NT9wwEB1RqNRygH5Qlc_60F6qWnVsJ3EOqELAahGwbdWtinoJ3thWV1oly2YXxJ_iyB_oH2OcbBZQJW4cqpwSR5YcP8-8ydjzAN5zzQSuv4jaTHIqlcY1F_UMDU2QWSmsSoyrxCbiTkednCTf5uCqOQvjt1U2NrEy1KbI_D_yz-hakKoIEUVfhmfUq0b57GojoVHD4tBeXmDIVm4f7OH8fuC8td_dbdOpqgDNeJSMaWzDjAtpGbeJcImJudC8Z1kPIwOZSCsjh5fRyNU1DqOH8ZJyngWgp0dubQX2-wQWpMBbfzK99X2WtYjDuFZMYIqiow_rLCq6SOFPJDPlnwWqouXqbi2H-z7xvkuo_Fxr-X_7Qi9gacqoyU69BF7CnM1fweLxrBxt-Rp-_7KDAR0WpTXespPCke6f_siQr77wKNmbisSgsRuQ_bO6-HlJ-jlp_732KubE1_Dq55NiUpIWEgHfTn4M_W62Ffj5KIN7A_N5kdu3QEzGtcT4jQnt0486caFjgdLMBTaImFuFT7MpTqemoUwx6vKISP9BxCp8bFCQDutSIw-9vNGA4LbrWwSsPdz8Dp61u8dH6dFB53AdniMJTOotOhswPx5N7CY8zc7H_XK0VQGcwOlj4-UG9QAv9Q |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Nb9QwEB2VLULtgc9W_QQf4IKw6thO4hwq1HZ31aqwrKCIikvwxra60irZbnaL-GMcuPLHGG-SLRVSbz2g3JLIkuPnmTeZ8TyAl1wzgfsvojaTnEqlcc9FA0NDE2RWCqsS4-ZiE3Gvp87Pk_4S_GrOwviyysYmzg21KTL_j3wPXQtSFSGiaM_VZRH9dvft-JJ6BSmfaW3kNCqInNof3zF8K_dP2rjWrzjvds6OjmmtMEAzHiVTGtsw40Jaxm0iXGJiLjQfWDbAKEEm0srI4WU08naNUxpg7KScZwTo9ZFnW4Hj3oPlGEmGbMHyYafX_7jIYcRhXOknMEXR7YdVThUdpvDnk5ny9wI1J-nq784ONz3kTQcx93rdR__z93oMD2uuTQ6qzfEElmz-FFbfLxrVls_g6xc7GtFxUVrjbT4pHDm7GE4M-eBbkpJ2LR-DZnBEOpdVW_SSDHNy_Pun1zcnvrvXMJ8Vs5J0kSL45-TT2Ne5rcHnO5ncOrTyIrcbQEzGtcTIjgntE5M6caFjgdLMBTaImNuEN4vlTmujUaYYj3l0pP-gYxNeN4hIx1UTktte3mkAcT30NRq2bn_8Ah4gTNJ3J73TbVhBdphUtTs70JpOZnYX7mdX02E5eV6jncC3uwbMH24qOgs |
| 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=Well-posedness+of+Third+Order+Differential+Equations+in+H%C3%B6lder+Continuous+Function+Spaces&rft.jtitle=Canadian+mathematical+bulletin&rft.au=Bu%2C+Shangquan&rft.au=Cai%2C+Gang&rft.date=2019-12-01&rft.pub=Canadian+Mathematical+Society&rft.issn=0008-4395&rft.eissn=1496-4287&rft.volume=62&rft.issue=4&rft.spage=715&rft.epage=726&rft_id=info:doi/10.4153%2FS0008439518000048&rft.externalDocID=10_4153_S0008439518000048 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0008-4395&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0008-4395&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0008-4395&client=summon |