Remark on local solvability of the Cauchy problem for semirelativistic equations

Nonexistence of local solutions to the Cauchy problem of semirelativistic equations with power type nonlinearity is shown in scale subcritical and one space dimension case. The nonexistence result is obtained by a transformation of semirelativistic equations and a test function method with test func...

Full description

Saved in:
Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 432; no. 2; pp. 744 - 748
Main Author Fujiwara, Kazumasa
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.12.2015
Subjects
Nonexistence of local solutions
Semirelativistic equation
Test function method
Nonexistence of local solutions
Semirelativistic equation
Test function method
Online AccessGet full text

Cover

Abstract Nonexistence of local solutions to the Cauchy problem of semirelativistic equations with power type nonlinearity is shown in scale subcritical and one space dimension case. The nonexistence result is obtained by a transformation of semirelativistic equations and a test function method with test functions which cancel the highest order derivatives.
AbstractList Nonexistence of local solutions to the Cauchy problem of semirelativistic equations with power type nonlinearity is shown in scale subcritical and one space dimension case. The nonexistence result is obtained by a transformation of semirelativistic equations and a test function method with test functions which cancel the highest order derivatives.
Author Fujiwara, Kazumasa
Author_xml – sequence: 1
  givenname: Kazumasa
  surname: Fujiwara
  fullname: Fujiwara, Kazumasa
  email: k-fujiwara@asagi.waseda.jp
  organization: Department of Pure and Applied Physics, Waseda University, 3-4-1, Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
BookMark eNp9kF1LwzAUhoNMcFP_gFf5A60naZO04I0Mv2CgiIJ3IUtPWGrbzKQb7N_bMa-9enkvnsN5nwWZDWFAQm4Y5AyYvG3ztjcm58BEDioHqM_InEEtM6hYMSNzAM4zXqqvC7JIqQVgTCg2J2_v2Jv4TcNAu2BNR1Po9mbtOz8eaHB03CBdmp3dHOg2hnWHPXUh0oS9j9iZ0e99Gr2l-LObShjSFTl3pkt4_ZeX5PPx4WP5nK1en16W96vMlhWMWa3QKTBMVFxUaKSwVVWbsuFFI6R0VrGCOVtLwUSh1gUrsFTSGS6NEWXZuOKS8NNdG0NKEZ3eRj9NOWgG-uhEt_roRB-daFB6cjJBdycIp8_2HqNO1uNgsZnW2FE3wf-H_wLBsm0i
CitedBy_id crossref_primary_10_1016_j_aml_2021_107619
crossref_primary_10_1007_s00028_016_0364_0
crossref_primary_10_1007_s00028_022_00865_9
crossref_primary_10_1002_mma_4944
crossref_primary_10_1016_j_matpur_2019_10_003
Cites_doi 10.1007/s00205-013-0620-1
10.1063/1.4746806
10.1063/1.4726198
10.1016/j.jmaa.2015.01.003
10.3934/cpaa.2015.14.1343
10.1137/060653688
10.1002/cpa.3160330403
ContentType Journal Article
Copyright 2015 Elsevier Inc.
Copyright_xml – notice: 2015 Elsevier Inc.
DBID AAYXX
CITATION
DOI 10.1016/j.jmaa.2015.07.009
DatabaseName CrossRef
DatabaseTitle CrossRef
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISSN 1096-0813
EndPage 748
ExternalDocumentID 10_1016_j_jmaa_2015_07_009
S0022247X15006447
GroupedDBID --K
--M
--Z
-~X
.~1
0R~
0SF
1B1
1RT
1~.
4.4
457
4G.
5GY
5VS
6I.
71M
85S
8P~
9JN
AABNK
AACTN
AAEDT
AAEDW
AAFTH
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AASFE
AAXUO
ABAOU
ABJNI
ABMAC
ABVKL
ABYKQ
ACAZW
ACDAQ
ACGFS
ACRLP
ADBBV
ADEZE
AEBSH
AEKER
AENEX
AEXQZ
AFKWA
AFTJW
AGUBO
AGYEJ
AHHHB
AIEXJ
AIGVJ
AIKHN
AITUG
AJBFU
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
ARUGR
AXJTR
BKOJK
BLXMC
CS3
DM4
EBS
EFBJH
EFLBG
EJD
EO8
EO9
EP2
EP3
F5P
FDB
FEDTE
FIRID
FNPLU
FYGXN
G-Q
GBLVA
HVGLF
IHE
IXB
J1W
KOM
LG5
M25
M41
MCRUF
MHUIS
MO0
N9A
NCXOZ
O-L
O9-
OAUVE
OK1
OZT
P-8
P-9
P2P
PC.
Q38
RIG
RNS
ROL
RPZ
SDF
SDG
SDP
SES
SPC
SPCBC
SSW
SSZ
T5K
TN5
TWZ
UPT
WH7
XPP
YQT
ZMT
ZU3
~G-
1~5
29L
6TJ
7-5
AAQXK
AAXKI
AAYXX
ABEFU
ABFNM
ABXDB
ADFGL
ADIYS
ADMUD
ADVLN
AFFNX
AFJKZ
AGHFR
AI.
AKRWK
ASPBG
AVWKF
AZFZN
CAG
CITATION
COF
FGOYB
G-2
G8K
HZ~
H~9
MVM
OHT
R2-
SEW
VH1
VOH
WUQ
XOL
YYP
ZCG
ID FETCH-LOGICAL-c480t-97ef70a158258ea65c889a4d23d566fc7131fc9651537b313e476fa26aa544df3
IEDL.DBID IXB
ISSN 0022-247X
IngestDate Thu Sep 26 15:55:15 EDT 2024
Fri Feb 23 02:33:01 EST 2024
IsDoiOpenAccess false
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 2
Keywords Nonexistence of local solutions
Semirelativistic equation
Test function method
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c480t-97ef70a158258ea65c889a4d23d566fc7131fc9651537b313e476fa26aa544df3
OpenAccessLink https://doi.org/10.1016/j.jmaa.2015.07.009
PageCount 5
ParticipantIDs crossref_primary_10_1016_j_jmaa_2015_07_009
elsevier_sciencedirect_doi_10_1016_j_jmaa_2015_07_009
PublicationCentury 2000
PublicationDate 2015-12-15
PublicationDateYYYYMMDD 2015-12-15
PublicationDate_xml – month: 12
  year: 2015
  text: 2015-12-15
  day: 15
PublicationDecade 2010
PublicationTitle Journal of mathematical analysis and applications
PublicationYear 2015
Publisher Elsevier Inc
Publisher_xml – name: Elsevier Inc
References Guo, Huang (br0060) 2012; 53
Kato (br0110) 1980; 33
K. Fujiwara, T. Ozawa, Remarks on global solutions to the Cauchy problem for semirelativistic equations with power type nonlinearity, unpublished.
T. Inui, Some nonexistence results for a semirelativistic Schrödinger equation with nongauge power type nonlinearity, unpublished.
Krieger, Lenzmann, Raphaël (br0120) 2013; 209
Ikeda, Inui (br0080) 2015
Fujita (br0030) 1970; vol. XVIII
Cho, Ozawa (br0020) 2006; 38
Ikeda, Inui (br0070) 2015; 425
Ikeda, Wakasugi (br0090) 2013; 26
Borgna, Rial (br0010) 2012; 53
Fujiwara, Machihara, Ozawa (br0040) 2015; 14
Cho (10.1016/j.jmaa.2015.07.009_br0020) 2006; 38
10.1016/j.jmaa.2015.07.009_br0100
Ikeda (10.1016/j.jmaa.2015.07.009_br0070) 2015; 425
Krieger (10.1016/j.jmaa.2015.07.009_br0120) 2013; 209
Fujita (10.1016/j.jmaa.2015.07.009_br0030) 1970; vol. XVIII
Guo (10.1016/j.jmaa.2015.07.009_br0060) 2012; 53
Borgna (10.1016/j.jmaa.2015.07.009_br0010) 2012; 53
10.1016/j.jmaa.2015.07.009_br0050
Ikeda (10.1016/j.jmaa.2015.07.009_br0080) 2015
Ikeda (10.1016/j.jmaa.2015.07.009_br0090) 2013; 26
Kato (10.1016/j.jmaa.2015.07.009_br0110) 1980; 33
Fujiwara (10.1016/j.jmaa.2015.07.009_br0040) 2015; 14
References_xml – volume: 53
  start-page: 062301
  year: 2012
  ident: br0010
  article-title: Existence of ground states for a one-dimensional relativistic Schrödinger equation
  publication-title: J. Math. Phys.
  contributor:
    fullname: Rial
– volume: vol. XVIII
  start-page: 105
  year: 1970
  end-page: 113
  ident: br0030
  article-title: On some nonexistence and nonuniqueness theorems for nonlinear parabolic equations
  publication-title: Nonlinear Functional Analysis
  contributor:
    fullname: Fujita
– volume: 26
  start-page: 1275
  year: 2013
  end-page: 1285
  ident: br0090
  article-title: Small-data blow-up of
  publication-title: Differential Integral Equations
  contributor:
    fullname: Wakasugi
– volume: 53
  start-page: 083702
  year: 2012
  ident: br0060
  article-title: Existence and stability of standing waves for nonlinear fractional Schrödinger equations
  publication-title: J. Math. Phys.
  contributor:
    fullname: Huang
– volume: 209
  start-page: 61
  year: 2013
  end-page: 129
  ident: br0120
  article-title: Nondispersive solutions to the
  publication-title: Arch. Ration. Mech. Anal.
  contributor:
    fullname: Raphaël
– volume: 38
  start-page: 1060
  year: 2006
  end-page: 1074
  ident: br0020
  article-title: On the semirelativistic Hartree-type equation
  publication-title: SIAM J. Math. Anal.
  contributor:
    fullname: Ozawa
– start-page: 1
  year: 2015
  end-page: 11
  ident: br0080
  article-title: Small data blow up of
  publication-title: J. Evol. Equ.
  contributor:
    fullname: Inui
– volume: 425
  start-page: 758
  year: 2015
  end-page: 773
  ident: br0070
  article-title: Some non-existence results for the semilinear Schrödinger equation without gauge invariance
  publication-title: J. Math. Anal. Appl.
  contributor:
    fullname: Inui
– volume: 33
  start-page: 501
  year: 1980
  end-page: 505
  ident: br0110
  article-title: Blow-up of solutions of some nonlinear hyperbolic equations
  publication-title: Comm. Pure Appl. Math.
  contributor:
    fullname: Kato
– volume: 14
  start-page: 1343
  year: 2015
  end-page: 1355
  ident: br0040
  article-title: On a system of semirelativistic equations in the energy space
  publication-title: Commun. Pure Appl. Anal.
  contributor:
    fullname: Ozawa
– ident: 10.1016/j.jmaa.2015.07.009_br0050
– volume: 209
  start-page: 61
  issue: 1
  year: 2013
  ident: 10.1016/j.jmaa.2015.07.009_br0120
  article-title: Nondispersive solutions to the L2-critical half-wave equation
  publication-title: Arch. Ration. Mech. Anal.
  doi: 10.1007/s00205-013-0620-1
  contributor:
    fullname: Krieger
– volume: 53
  start-page: 083702
  issue: 8
  year: 2012
  ident: 10.1016/j.jmaa.2015.07.009_br0060
  article-title: Existence and stability of standing waves for nonlinear fractional Schrödinger equations
  publication-title: J. Math. Phys.
  doi: 10.1063/1.4746806
  contributor:
    fullname: Guo
– ident: 10.1016/j.jmaa.2015.07.009_br0100
– start-page: 1
  year: 2015
  ident: 10.1016/j.jmaa.2015.07.009_br0080
  article-title: Small data blow up of L2 or H1-solution for the semilinear Schrödinger equation without gauge invariance
  publication-title: J. Evol. Equ.
  contributor:
    fullname: Ikeda
– volume: 26
  start-page: 1275
  issue: 11–12
  year: 2013
  ident: 10.1016/j.jmaa.2015.07.009_br0090
  article-title: Small-data blow-up of L2-solution for the nonlinear Schrödinger equation without gauge invariance
  publication-title: Differential Integral Equations
  contributor:
    fullname: Ikeda
– volume: 53
  start-page: 062301
  issue: 6
  year: 2012
  ident: 10.1016/j.jmaa.2015.07.009_br0010
  article-title: Existence of ground states for a one-dimensional relativistic Schrödinger equation
  publication-title: J. Math. Phys.
  doi: 10.1063/1.4726198
  contributor:
    fullname: Borgna
– volume: 425
  start-page: 758
  issue: 2
  year: 2015
  ident: 10.1016/j.jmaa.2015.07.009_br0070
  article-title: Some non-existence results for the semilinear Schrödinger equation without gauge invariance
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/j.jmaa.2015.01.003
  contributor:
    fullname: Ikeda
– volume: vol. XVIII
  start-page: 105
  year: 1970
  ident: 10.1016/j.jmaa.2015.07.009_br0030
  article-title: On some nonexistence and nonuniqueness theorems for nonlinear parabolic equations
  contributor:
    fullname: Fujita
– volume: 14
  start-page: 1343
  issue: 4
  year: 2015
  ident: 10.1016/j.jmaa.2015.07.009_br0040
  article-title: On a system of semirelativistic equations in the energy space
  publication-title: Commun. Pure Appl. Anal.
  doi: 10.3934/cpaa.2015.14.1343
  contributor:
    fullname: Fujiwara
– volume: 38
  start-page: 1060
  issue: 4
  year: 2006
  ident: 10.1016/j.jmaa.2015.07.009_br0020
  article-title: On the semirelativistic Hartree-type equation
  publication-title: SIAM J. Math. Anal.
  doi: 10.1137/060653688
  contributor:
    fullname: Cho
– volume: 33
  start-page: 501
  issue: 4
  year: 1980
  ident: 10.1016/j.jmaa.2015.07.009_br0110
  article-title: Blow-up of solutions of some nonlinear hyperbolic equations
  publication-title: Comm. Pure Appl. Math.
  doi: 10.1002/cpa.3160330403
  contributor:
    fullname: Kato
SSID ssj0011571
Score 2.2412503
Snippet Nonexistence of local solutions to the Cauchy problem of semirelativistic equations with power type nonlinearity is shown in scale subcritical and one space...
SourceID crossref
elsevier
SourceType Aggregation Database
Publisher
StartPage 744
SubjectTerms Nonexistence of local solutions
Semirelativistic equation
Test function method
Title Remark on local solvability of the Cauchy problem for semirelativistic equations
URI https://dx.doi.org/10.1016/j.jmaa.2015.07.009
Volume 432
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3JTsMwELVKucABsYqyVD5wQ4FMY2c5thVVIbRCFYXcIsd1RIualm5SL3w7niwVSIgDJyeRHUUTZ944nveGkCupmOeC8vSX5giDSZMZrlLKAAEKXImIi_87Ol273WcPAQ9KpFlwYTCtMvf9mU9PvXV-5Ta35u10OESOr8Y25gQ6pNG4ypBRbml0RhJf0NjsJAB3oFAMx945cSbL8RqNBWoPAU8FPDEp8Tdw-gY4rX2yl0eKtJ49zAEpqeSQ7HY2MqvzI_LU04ezdzpJaIpJVE-kVSa8vaaTmOqutCmW8m1N88IxVMeodK7Gw4zDskplmqn6yAS_58ek37p7braNvESCIZlrLgzPUbFjCuB6oecqYXPpup5gg5o10HFaLPUSFGLpYb1zy4kssBRz7FjUbCE4Y4PYOiHlZJKoU0IHALbGbgDl2ixm4ClL39wWDo-YqFlRhVwXtgmnmRJGWKSIjUK0ZIiWDE3c0PYqhBfmC3-8z1C76j_Gnf1z3DnZwTNMNAF-QcqL2VJd6nBhEVXJ1s0nVMl2vfHiP2J777e72Pq9V7-azpYv-nbC7A
link.rule.ids 315,783,787,3515,4511,24130,27583,27938,27939,45599,45677,45693,45888
linkProvider Elsevier
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3JTsMwELVKewAOiFWU1QduKGrc2HFyLBVVoYsQalFvluM6okVNSzepf884cSqQEAduUZKJookz740984zQndI0DIgO4U_j0qHKpU6gtXaIJJoEyiCume_odP1mnz4P2KCA6nkvjCmrtLE_i-lptLZnKtabldloZHp8AdsoHwClAVylfAeVgA1wyMBKtYe3Vnu7mEAYJ7louDGwvTNZmdd4Io38EGGphqepS_wNn75hTuMQHViyiGvZ-xyhgk6O0X5nq7S6OEEvr3A4_8DTBKewhGEsrTPt7Q2exhhuxXW5Uu8bbPeOwUBT8UJPRlkbyzpVasb6M9P8XpyifuOxV286dpcER9HAXToh1zF3JWGQ6wVa-kwFQSjpsOoNgarFCrJQEqvQbHnu8cgjnqbcj2XVl5JROoy9M1RMpok-R3hIiA_wTYgOfBpTEmoPHu5LziIqq15URve5b8QsE8MQeZXYWBhPCuNJ4Zo17bCMWO4-8eOTCojWf9hd_NPuFu02e522aD91W5doz1wxdSeEXaHicr7S18AeltGNHR1fIUzBcg
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=Remark+on+local+solvability+of+the+Cauchy+problem+for+semirelativistic+equations&rft.jtitle=Journal+of+mathematical+analysis+and+applications&rft.au=Fujiwara%2C+Kazumasa&rft.date=2015-12-15&rft.pub=Elsevier+Inc&rft.issn=0022-247X&rft.eissn=1096-0813&rft.volume=432&rft.issue=2&rft.spage=744&rft.epage=748&rft_id=info:doi/10.1016%2Fj.jmaa.2015.07.009&rft.externalDocID=S0022247X15006447
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0022-247X&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0022-247X&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0022-247X&client=summon