Exact boundary controllability for quasilinear wave equations in a planar tree-like network of strings

In this paper the local exact boundary controllability for quasilinear wave equations on a planar tree-like network of strings is established and the number of boundary controls is equal to the number of simple nodes minus 1.

Saved in:
Bibliographic Details
Published inAnnales de l'Institut Henri Poincaré. Analyse non linéaire Vol. 26; no. 6; pp. 2373 - 2384
Main Authors Gu, Qilong, Li, Tatsien
Format Journal Article
LanguageEnglish
Published Paris Elsevier Masson SAS 01.11.2009
Elsevier
Subjects
Combinatorics
Combinatorics. Ordered structures
Exact boundary controllability
Exact sciences and technology
Graph theory
Mathematical analysis
Mathematics
Partial differential equations
Planar tree-like network of strings
Quasilinear wave equation
Sciences and techniques of general use
Planar tree-like network of strings
35L05
Exact boundary controllability
93B05
Quasilinear wave equation
Wave equation
Boundary control
Mathematics
Nonlinear analysis
Online AccessGet full text

Cover

Abstract In this paper the local exact boundary controllability for quasilinear wave equations on a planar tree-like network of strings is established and the number of boundary controls is equal to the number of simple nodes minus 1.
AbstractList In this paper the local exact boundary controllability for quasilinear wave equations on a planar tree-like network of strings is established and the number of boundary controls is equal to the number of simple nodes minus 1.
Author Gu, Qilong
Li, Tatsien
Author_xml – sequence: 1
  givenname: Qilong
  surname: Gu
  fullname: Gu, Qilong
  email: ql_gu@yahoo.com.cn
  organization: School of Mathematical Sciences, Fudan University, Shanghai 200433, China
– sequence: 2
  givenname: Tatsien
  surname: Li
  fullname: Li, Tatsien
  email: dqli@fudan.edu.cn
  organization: School of Mathematical Sciences, Fudan University, Shanghai 200433, China
BackLink http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=22205057$$DView record in Pascal Francis
BookMark eNp9kMlKBDEQhoMoOC5v4CEXj91W0msugogbCF70HKrT1ZqZNhmTuL29GUY8eqr1r-L_Dtiu844YOxFQChDt2bJEZ1_WppQAqoSmBJA7bCH6ripEXcEuW4BUdc5rtc8OYlwCQAdNu2DT1ReaxAf_7kYM39x4l4KfZxzsbNM3n3zgb-8Yc-UIA__ED-KUO8l6F7l1HPl6RpdHKRAVs10Rd5Q-fVhxP_GYgnXP8YjtTThHOv6Nh-zp-urx8ra4f7i5u7y4L0zVy1QMzSjQ1EKArFWnhFSmq6GtKjBTTapvoVMd9qiQxNgMlRF9A72AVow0COyrQ1Zv75rgYww06XWwr9mYFqA3rPRSb1npDSsNjc6ssux0K1tjNDhPAZ2x8U8rpYQGmi7vnW_3KHv4sBR0NJacodEGMkmP3v7_6AfpN4Q3
CitedBy_id crossref_primary_10_2478_candc_2023_0033
crossref_primary_10_1007_s11425_015_5107_0
crossref_primary_10_1016_j_matpur_2010_06_001
crossref_primary_10_1016_j_matpur_2012_06_004
crossref_primary_10_1002_mma_1410
crossref_primary_10_1002_mma_2881
crossref_primary_10_1007_s11401_011_0693_9
crossref_primary_10_1007_s11401_013_0785_9
Cites_doi 10.1137/1020095
10.1137/S0363012901390099
10.1016/S1631-073X(03)00327-3
10.57262/die/1356060252
10.1007/s10883-005-4169-7
10.1142/S0252959902000201
10.1137/S0363012903427300
10.1007/BF01442394
10.1142/S0252959901000334
10.3934/nhm.2007.2.425
10.1137/0330015
10.3934/dcds.2002.8.469
10.1137/1030001
10.1070/RM1989v044n03ABEH002111
10.1007/s10492-007-0018-1
10.1016/S0294-1449(16)30221-9
ContentType Journal Article
Copyright 2009 2009 L'Association Publications de l'Institut Henri Poincaré. Published by Elsevier B.V.
2015 INIST-CNRS
Copyright_xml – notice: 2009 2009 L'Association Publications de l'Institut Henri Poincaré. Published by Elsevier B.V.
– notice: 2015 INIST-CNRS
DBID 6I.
AAFTH
IQODW
AAYXX
CITATION
DOI 10.1016/j.anihpc.2009.05.002
DatabaseName ScienceDirect Open Access Titles
Elsevier:ScienceDirect:Open Access
Pascal-Francis
CrossRef
DatabaseTitle CrossRef
DatabaseTitleList CrossRef
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
Mathematics
Physics
EISSN 1873-1430
EndPage 2384
ExternalDocumentID 10_1016_j_anihpc_2009_05_002
22205057
S0294144909000493
GroupedDBID --K
--M
-~X
.~1
0R~
1B1
1~.
1~5
4.4
457
4G.
5GY
5VS
692
6I.
7-5
71M
8P~
AACTN
AAEDT
AAEDW
AAFTH
AAFWJ
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AAQXK
AAXUO
ABAOU
ABMAC
ABVKL
ABXDB
ACDAQ
ACRLP
ADBBV
ADEZE
ADMUD
AEKER
AEXQZ
AFKWA
AFPKN
AFTJW
AGHFR
AGUBO
AGYEJ
AI.
AIGVJ
AIKHN
AITUG
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
ARUGR
ASPBG
AVWKF
AZFZN
BKOJK
BLXMC
CS3
EBS
EFLBG
EJD
EO8
EO9
EP2
EP3
FAM
FDB
FEDTE
FGOYB
FIRID
FNPLU
FRP
G-Q
GBLVA
GROUPED_DOAJ
HVGLF
HZ~
IHE
IXB
J1W
KOM
LO0
M41
MO0
N9A
NCXOZ
O9-
OAUVE
OAV
OK1
OZT
P-8
P-9
PC.
Q38
R2-
REW
RIG
ROL
RPZ
SDF
SDG
SES
SEW
SPC
SPD
SSW
SSZ
T5K
TN5
VH1
~G-
ABPTK
IQODW
0SF
AAYXX
ADVLN
CITATION
ID FETCH-LOGICAL-c382t-b5d1ac411024979129c7406330cf4e9860797a8a9ae1d5b3c185081061deb1a83
IEDL.DBID ABVKL
ISSN 0294-1449
IngestDate Wed Oct 23 14:18:33 EDT 2024
Sun Oct 22 16:08:22 EDT 2023
Fri Feb 23 02:48:30 EST 2024
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 6
Keywords Planar tree-like network of strings
35L05
Exact boundary controllability
93B05
Quasilinear wave equation
Wave equation
Boundary control
Mathematics
Nonlinear analysis
Language English
License This article is made available under the Elsevier license.
CC BY 4.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c382t-b5d1ac411024979129c7406330cf4e9860797a8a9ae1d5b3c185081061deb1a83
OpenAccessLink https://www.sciencedirect.com/science/article/pii/S0294144909000493
PageCount 12
ParticipantIDs crossref_primary_10_1016_j_anihpc_2009_05_002
pascalfrancis_primary_22205057
elsevier_sciencedirect_doi_10_1016_j_anihpc_2009_05_002
PublicationCentury 2000
PublicationDate 2009-11-01
PublicationDateYYYYMMDD 2009-11-01
PublicationDate_xml – month: 11
  year: 2009
  text: 2009-11-01
  day: 01
PublicationDecade 2000
PublicationPlace Paris
PublicationPlace_xml – name: Paris
PublicationTitle Annales de l'Institut Henri Poincaré. Analyse non linéaire
PublicationYear 2009
Publisher Elsevier Masson SAS
Elsevier
Publisher_xml – name: Elsevier Masson SAS
– name: Elsevier
References Li, Jin (bib008) 2001; 22
Lasiecka, Triggiani (bib007) 1991; 23
Zuazua (bib019) 1990; 69
Emanuilov (bib005) 1989; 44
Nicaise, Valein (bib016) 2007; 2
Lions (bib014) 1988
Dáger, Zuazua (bib004) 2000; vol. 50
Li, Yu (bib013) 1985; vol. V
Zuazua (bib020) 1993; 10
Ammari, Jellouli (bib001) 2004; 17
Lions (bib015) 1988; 30
Li, Rao (bib009) 2003; 41
Li, Yu (bib011) 2003; 337
Zuazua (bib021) 2002; 8
Schmidt (bib018) 1992; 30
Ammari, Jellouli (bib002) 2007; 52
Russell (bib017) 1978; 20
Li, Rao (bib010) 2002; 23
Li, Yu (bib012) 2006; 45
Lagnese, Leugering, Schmidt (bib006) 1994
Ammari, Jellouli, Khenissi (bib003) 2005; 11
Emanuilov (10.1016/j.anihpc.2009.05.002_bib005) 1989; 44
Nicaise (10.1016/j.anihpc.2009.05.002_bib016) 2007; 2
Ammari (10.1016/j.anihpc.2009.05.002_bib001) 2004; 17
Li (10.1016/j.anihpc.2009.05.002_bib013) 1985; vol. V
Lagnese (10.1016/j.anihpc.2009.05.002_bib006) 1994
Li (10.1016/j.anihpc.2009.05.002_bib011) 2003; 337
Ammari (10.1016/j.anihpc.2009.05.002_bib003) 2005; 11
Zuazua (10.1016/j.anihpc.2009.05.002_bib021) 2002; 8
Li (10.1016/j.anihpc.2009.05.002_bib012) 2006; 45
Lions (10.1016/j.anihpc.2009.05.002_bib014) 1988
Li (10.1016/j.anihpc.2009.05.002_bib008) 2001; 22
Zuazua (10.1016/j.anihpc.2009.05.002_bib019) 1990; 69
Li (10.1016/j.anihpc.2009.05.002_bib009) 2003; 41
Schmidt (10.1016/j.anihpc.2009.05.002_bib018) 1992; 30
Li (10.1016/j.anihpc.2009.05.002_bib010) 2002; 23
Russell (10.1016/j.anihpc.2009.05.002_bib017) 1978; 20
Zuazua (10.1016/j.anihpc.2009.05.002_bib020) 1993; 10
Lasiecka (10.1016/j.anihpc.2009.05.002_bib007) 1991; 23
Lions (10.1016/j.anihpc.2009.05.002_bib015) 1988; 30
Dáger (10.1016/j.anihpc.2009.05.002_bib004) 2000; vol. 50
Ammari (10.1016/j.anihpc.2009.05.002_bib002) 2007; 52
References_xml – volume: 69
  start-page: 1
  year: 1990
  end-page: 31
  ident: bib019
  article-title: Exact controllability for the semilinear wave equation
  publication-title: J. Math. Pures Appl.
  contributor:
    fullname: Zuazua
– volume: 20
  start-page: 639
  year: 1978
  end-page: 739
  ident: bib017
  article-title: Controllability and stabilizability theory for linear partial differential equations, Recent progress and open questions
  publication-title: SIAM Rev.
  contributor:
    fullname: Russell
– volume: 11
  start-page: 177
  year: 2005
  end-page: 193
  ident: bib003
  article-title: Stabilization of generic trees of strings
  publication-title: J. Dyn. Control Syst.
  contributor:
    fullname: Khenissi
– volume: 22
  start-page: 325
  year: 2001
  end-page: 336
  ident: bib008
  article-title: Semi-global
  publication-title: Chinese Ann. Math. Ser. B
  contributor:
    fullname: Jin
– year: 1994
  ident: bib006
  article-title: Modeling, Analysis and Control of Multi-link Structures
  publication-title: Systems Control Found. Appl.
  contributor:
    fullname: Schmidt
– volume: 17
  start-page: 1395
  year: 2004
  end-page: 1410
  ident: bib001
  article-title: Stabilization of star-shaped networks of strings
  publication-title: Differential Integral Equations
  contributor:
    fullname: Jellouli
– volume: 52
  start-page: 327
  year: 2007
  end-page: 343
  ident: bib002
  article-title: Remark on stabilization of tree-shaped networks of strings
  publication-title: Appl. Math.
  contributor:
    fullname: Jellouli
– volume: 44
  start-page: 183
  year: 1989
  end-page: 184
  ident: bib005
  article-title: Boundary control by semilinear evolution equations
  publication-title: Russian Math. Surveys
  contributor:
    fullname: Emanuilov
– volume: 41
  start-page: 1748
  year: 2003
  end-page: 1755
  ident: bib009
  article-title: Exact boundary controllability for quasilinear hyperbolic systems
  publication-title: SIAM J. Control Optim.
  contributor:
    fullname: Rao
– year: 1988
  ident: bib014
  article-title: Contrôlabilité Exacte, Perturbations et Stabilisation de Systèmes Distribués, vol. I
  contributor:
    fullname: Lions
– volume: 8
  start-page: 469
  year: 2002
  end-page: 513
  ident: bib021
  article-title: Controllability of partial differential equations and its semi-discrete approximation
  publication-title: Discrete Contin. Dyn. Syst.
  contributor:
    fullname: Zuazua
– volume: 30
  start-page: 229
  year: 1992
  end-page: 245
  ident: bib018
  article-title: On the modeling and exact controllability of networks of vibrating strings
  publication-title: SIAM J. Control Optim.
  contributor:
    fullname: Schmidt
– volume: 10
  start-page: 109
  year: 1993
  end-page: 129
  ident: bib020
  article-title: Exact controllability for semilinear wave equations
  publication-title: Ann. Inst. H. Poincaré Anal. Non Linéaire
  contributor:
    fullname: Zuazua
– volume: 337
  start-page: 271
  year: 2003
  end-page: 276
  ident: bib011
  article-title: Contrôlabilité exacte frontière pour les équations des ondes quasi linéaires unidimensionnelles
  publication-title: C. R. Acad. Sci. Paris Sér. I
  contributor:
    fullname: Yu
– volume: 23
  start-page: 109
  year: 1991
  end-page: 154
  ident: bib007
  article-title: Exact controllability of semilinear abstract systems with applications to waves and plates boundary control problems
  publication-title: Appl. Math. Optim.
  contributor:
    fullname: Triggiani
– volume: vol. 50
  year: 2000
  ident: bib004
  article-title: Wave Propagation, Observation and Control in 1-D Flexible Multi-structures
  publication-title: Math. Appl.
  contributor:
    fullname: Zuazua
– volume: 23
  start-page: 209
  year: 2002
  end-page: 218
  ident: bib010
  article-title: Local exact boundary controllability for a class of quasilinear hyperbolic systems
  publication-title: Chinese Ann. Math. Ser. B
  contributor:
    fullname: Rao
– volume: 30
  start-page: 1
  year: 1988
  end-page: 68
  ident: bib015
  article-title: Exact controllability, stabilization and perturbations for distributed systems
  publication-title: SIAM Rev.
  contributor:
    fullname: Lions
– volume: 45
  start-page: 1074
  year: 2006
  end-page: 1083
  ident: bib012
  article-title: Exact boundary controllability for 1-D quasilinear wave equations
  publication-title: SIAM J. Control Optim.
  contributor:
    fullname: Yu
– volume: vol. V
  year: 1985
  ident: bib013
  article-title: Boundary Value Problems for Quasilinear Hyperbolic Systems
  publication-title: Duke Univ. Math. Ser.
  contributor:
    fullname: Yu
– volume: 2
  start-page: 425
  year: 2007
  end-page: 479
  ident: bib016
  article-title: Stabilization of the wave equation on 1-D networks with a delay term in the nodal feedbacks
  publication-title: Netw. Heterog. Media
  contributor:
    fullname: Valein
– year: 1994
  ident: 10.1016/j.anihpc.2009.05.002_bib006
  article-title: Modeling, Analysis and Control of Multi-link Structures
  contributor:
    fullname: Lagnese
– volume: 20
  start-page: 639
  year: 1978
  ident: 10.1016/j.anihpc.2009.05.002_bib017
  article-title: Controllability and stabilizability theory for linear partial differential equations, Recent progress and open questions
  publication-title: SIAM Rev.
  doi: 10.1137/1020095
  contributor:
    fullname: Russell
– volume: 41
  start-page: 1748
  year: 2003
  ident: 10.1016/j.anihpc.2009.05.002_bib009
  article-title: Exact boundary controllability for quasilinear hyperbolic systems
  publication-title: SIAM J. Control Optim.
  doi: 10.1137/S0363012901390099
  contributor:
    fullname: Li
– volume: 337
  start-page: 271
  year: 2003
  ident: 10.1016/j.anihpc.2009.05.002_bib011
  article-title: Contrôlabilité exacte frontière pour les équations des ondes quasi linéaires unidimensionnelles
  publication-title: C. R. Acad. Sci. Paris Sér. I
  doi: 10.1016/S1631-073X(03)00327-3
  contributor:
    fullname: Li
– volume: 17
  start-page: 1395
  year: 2004
  ident: 10.1016/j.anihpc.2009.05.002_bib001
  article-title: Stabilization of star-shaped networks of strings
  publication-title: Differential Integral Equations
  doi: 10.57262/die/1356060252
  contributor:
    fullname: Ammari
– volume: 11
  start-page: 177
  year: 2005
  ident: 10.1016/j.anihpc.2009.05.002_bib003
  article-title: Stabilization of generic trees of strings
  publication-title: J. Dyn. Control Syst.
  doi: 10.1007/s10883-005-4169-7
  contributor:
    fullname: Ammari
– volume: 23
  start-page: 209
  year: 2002
  ident: 10.1016/j.anihpc.2009.05.002_bib010
  article-title: Local exact boundary controllability for a class of quasilinear hyperbolic systems
  publication-title: Chinese Ann. Math. Ser. B
  doi: 10.1142/S0252959902000201
  contributor:
    fullname: Li
– volume: 69
  start-page: 1
  year: 1990
  ident: 10.1016/j.anihpc.2009.05.002_bib019
  article-title: Exact controllability for the semilinear wave equation
  publication-title: J. Math. Pures Appl.
  contributor:
    fullname: Zuazua
– volume: vol. 50
  year: 2000
  ident: 10.1016/j.anihpc.2009.05.002_bib004
  article-title: Wave Propagation, Observation and Control in 1-D Flexible Multi-structures
  contributor:
    fullname: Dáger
– year: 1988
  ident: 10.1016/j.anihpc.2009.05.002_bib014
  contributor:
    fullname: Lions
– volume: 45
  start-page: 1074
  year: 2006
  ident: 10.1016/j.anihpc.2009.05.002_bib012
  article-title: Exact boundary controllability for 1-D quasilinear wave equations
  publication-title: SIAM J. Control Optim.
  doi: 10.1137/S0363012903427300
  contributor:
    fullname: Li
– volume: 23
  start-page: 109
  year: 1991
  ident: 10.1016/j.anihpc.2009.05.002_bib007
  article-title: Exact controllability of semilinear abstract systems with applications to waves and plates boundary control problems
  publication-title: Appl. Math. Optim.
  doi: 10.1007/BF01442394
  contributor:
    fullname: Lasiecka
– volume: 22
  start-page: 325
  year: 2001
  ident: 10.1016/j.anihpc.2009.05.002_bib008
  article-title: Semi-global C1 solution to the mixed initial–boundary value problem for quasilinear hyperbolic systems
  publication-title: Chinese Ann. Math. Ser. B
  doi: 10.1142/S0252959901000334
  contributor:
    fullname: Li
– volume: 2
  start-page: 425
  year: 2007
  ident: 10.1016/j.anihpc.2009.05.002_bib016
  article-title: Stabilization of the wave equation on 1-D networks with a delay term in the nodal feedbacks
  publication-title: Netw. Heterog. Media
  doi: 10.3934/nhm.2007.2.425
  contributor:
    fullname: Nicaise
– volume: 30
  start-page: 229
  year: 1992
  ident: 10.1016/j.anihpc.2009.05.002_bib018
  article-title: On the modeling and exact controllability of networks of vibrating strings
  publication-title: SIAM J. Control Optim.
  doi: 10.1137/0330015
  contributor:
    fullname: Schmidt
– volume: 8
  start-page: 469
  year: 2002
  ident: 10.1016/j.anihpc.2009.05.002_bib021
  article-title: Controllability of partial differential equations and its semi-discrete approximation
  publication-title: Discrete Contin. Dyn. Syst.
  doi: 10.3934/dcds.2002.8.469
  contributor:
    fullname: Zuazua
– volume: 30
  start-page: 1
  year: 1988
  ident: 10.1016/j.anihpc.2009.05.002_bib015
  article-title: Exact controllability, stabilization and perturbations for distributed systems
  publication-title: SIAM Rev.
  doi: 10.1137/1030001
  contributor:
    fullname: Lions
– volume: 44
  start-page: 183
  year: 1989
  ident: 10.1016/j.anihpc.2009.05.002_bib005
  article-title: Boundary control by semilinear evolution equations
  publication-title: Russian Math. Surveys
  doi: 10.1070/RM1989v044n03ABEH002111
  contributor:
    fullname: Emanuilov
– volume: 52
  start-page: 327
  year: 2007
  ident: 10.1016/j.anihpc.2009.05.002_bib002
  article-title: Remark on stabilization of tree-shaped networks of strings
  publication-title: Appl. Math.
  doi: 10.1007/s10492-007-0018-1
  contributor:
    fullname: Ammari
– volume: vol. V
  year: 1985
  ident: 10.1016/j.anihpc.2009.05.002_bib013
  article-title: Boundary Value Problems for Quasilinear Hyperbolic Systems
  contributor:
    fullname: Li
– volume: 10
  start-page: 109
  year: 1993
  ident: 10.1016/j.anihpc.2009.05.002_bib020
  article-title: Exact controllability for semilinear wave equations
  publication-title: Ann. Inst. H. Poincaré Anal. Non Linéaire
  doi: 10.1016/S0294-1449(16)30221-9
  contributor:
    fullname: Zuazua
SSID ssj0007056
Score 1.9442285
Snippet In this paper the local exact boundary controllability for quasilinear wave equations on a planar tree-like network of strings is established and the number of...
SourceID crossref
pascalfrancis
elsevier
SourceType Aggregation Database
Index Database
Publisher
StartPage 2373
SubjectTerms Combinatorics
Combinatorics. Ordered structures
Exact boundary controllability
Exact sciences and technology
Graph theory
Mathematical analysis
Mathematics
Partial differential equations
Planar tree-like network of strings
Quasilinear wave equation
Sciences and techniques of general use
Title Exact boundary controllability for quasilinear wave equations in a planar tree-like network of strings
URI https://dx.doi.org/10.1016/j.anihpc.2009.05.002
Volume 26
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LT4QwEJ74iInGGJ_xuenBa90uhS0cdaPx7cFHNl5IKUXRDYvL-rr4250WWDUxMfFYoECmZeYr_eYbgO1ARMLTDqc4gX3qtnlM_YhxqlWimJcoN7FswrPz9uG1e9z1umPQqXNhDK2y8v2lT7feujrSrKzZzNO0ecmcwMXlQMACi3P5OEw6iH7x65zc3bs5OR05ZMFsEVdzPTUd6gw6S_OSWXqfq0q48uv_yi8RajaXBdotKQtefItCB_MwV8FHslu-4QKM6WwRZr6JCmLrbKTEWizClKV4qmIJkv03qYYksnWUBu-kIqn3SqHud4LolTw9yyI1wFMOyKt80UQ_lVLgBUkzIknekxmeMjvZtJc-apKVLHLST4gpAJLdFctwfbB_1TmkVZUFqrjvDGnkxS2pXIQBuBITAcZ_JTDKc85U4urAbzMRCOkbFe9W7EVcYYRHHIE4IEY_L32-AhNZP9OrQBDtCYmISDmau0y1IwTDMlJx7Eitcdm7BrS2bJiXYhphzTJ7CMuRMHUxg5B5IY7EGoja_OGPSRGiv_-jZ-PHaI0e55jEYsSo6_--9QZM2x0lm4-4CRPDwbPeQmAyjBowvvPRalTTD1tH3T1snXe6F7efHDrl5A
link.rule.ids 315,783,787,3513,4509,27581,27936,27937,45597,45675,45886
linkProvider Elsevier
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3JTsMwEB2xCAFCiFWsxQeuVk2c1MkREKhAywWQeoscx4FAlaZNy_L3jJ2kgISExDGJs2g8mnmO37wBOA5EJDztcIoO7FO3xWPqR4xTrRLFvES5iWUTdm9b7Qf3uuf1ZuC8roUxtMoq9pcx3Ubr6kyzsmYzT9PmHXMCF5cDAQsszuWzMG_KLo2bX_XOpuFYMNvC1YymZnhdP2dJXjJLn3JVyVZ-_V35JT-t5LJAqyVlu4tvOehyDVYr8EhOy-9bhxmdbcDyN0lBPOpOdViLDViwBE9VbEJy8S7VmES2i9Log1QU9X4p0_1BELuS4UQWqYGdckTe5KsmelgKgRckzYgkeV9meMnsY9N--qJJVnLIySAhpv1H9lhswcPlxf15m1Y9FqjivjOmkRefSOUiCMB1mAgw-yuBOZ5zphJXB36LiUBI32h4n8RexBXmd0QRiAJijPLS59swlw0yvQMEsZ6QiIeUo7nLVCtCKCwjFceO1BoXvbtAa8uGeSmlEdYcs-ewnAnTFTMImRfiTOyCqM0f_nCJEKP9H3c2fszW9HWOKStGhLr370cfwWL7vtsJO1e3N_uwZPeWbGXiAcyNRxN9iBBlHDWsC34Co4TkAQ
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=Exact+boundary+controllability+for+quasilinear+wave+equations+in+a+planar+tree-like+network+of+strings&rft.jtitle=Annales+de+l%27Institut+Henri+Poincar%C3%A9.+Analyse+non+lin%C3%A9aire&rft.au=QILONG+GU&rft.au=TATSIEN+LI&rft.date=2009-11-01&rft.pub=Elsevier&rft.issn=0294-1449&rft.eissn=1873-1430&rft.volume=26&rft.issue=6&rft.spage=2373&rft.epage=2384&rft_id=info:doi/10.1016%2Fj.anihpc.2009.05.002&rft.externalDBID=n%2Fa&rft.externalDocID=22205057
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0294-1449&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0294-1449&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0294-1449&client=summon