Global weak solutions to the weakly dissipative Degasperis–Procesi equation
The global weak solutions for the Degasperis–Procesi equation with weakly dissipative term are investigated. Provided that u 0 ∈ H 1 ( R ) , y 0 = ( 1 − ∂ x 2 ) u 0 ∈ M ( R ) , supp y 0 − ⊂ ( − ∞ , x 0 ) and supp y 0 + ⊂ ( x 0 , ∞ ) , the existence and uniqueness of global weak solutions for the equ...
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| Veröffentlicht in: | Nonlinear analysis 2011-10, Vol.74 (15), p.4961-4973 |
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| container_title | Nonlinear analysis |
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| creator | Guo, Yunxi Lai, Shaoyong Wang, Ying |
| description | The global weak solutions for the Degasperis–Procesi equation with weakly dissipative term are investigated. Provided that
u
0
∈
H
1
(
R
)
,
y
0
=
(
1
−
∂
x
2
)
u
0
∈
M
(
R
)
,
supp
y
0
−
⊂
(
−
∞
,
x
0
)
and
supp
y
0
+
⊂
(
x
0
,
∞
)
, the existence and uniqueness of global weak solutions for the equation are shown to be true in the space
W
l
o
c
1
,
∞
(
R
+
×
R
)
∩
L
l
o
c
∞
(
R
+
;
H
1
(
R
)
)
. |
| doi_str_mv | 10.1016/j.na.2011.04.051 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_889428706</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0362546X11002550</els_id><sourcerecordid>889428706</sourcerecordid><originalsourceid>FETCH-LOGICAL-c356t-b285a46ad34feb160780e99ef00e30477367907855aaff2d2b1651bdb8cfeac33</originalsourceid><addsrcrecordid>eNp1kM9KxEAMxgdRcF29e-xFPLVm2k7b9Sb-B0UPCt6GdJrqrN3OOukq3nwH39AncdYVb0IgEH7fl-QTYldCIkEWB9OkxyQFKRPIE1ByTYxkVWaxSqVaFyPIijRWefGwKbaYpwAgy6wYievzztXYRW-EzxG7bjFY13M0uGh4op9p9x41ltnOcbCvFJ3QI_KcvOWvj89b7wyxjehlgUvhtthosWPa-e1jcX92end8EV_dnF8eH13FJlPFENdppTAvsMnylmpZQFkBTSbUAlAGeRkuKydhqBRi26ZNGhgl66auTEtosmws9le-c-9eFsSDnlk21HXYk1uwrqpJnlYlFIGEFWm8Y_bU6rm3M_TvWoJeBqenuke9DE5DrkNwQbL3a45ssGs99sbyny4NzipU4A5XHIVPXy15zcZSb6ixnsygG2f_X_INmI2D3g</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>889428706</pqid></control><display><type>article</type><title>Global weak solutions to the weakly dissipative Degasperis–Procesi equation</title><source>Elsevier ScienceDirect Journals Complete</source><creator>Guo, Yunxi ; Lai, Shaoyong ; Wang, Ying</creator><creatorcontrib>Guo, Yunxi ; Lai, Shaoyong ; Wang, Ying</creatorcontrib><description>The global weak solutions for the Degasperis–Procesi equation with weakly dissipative term are investigated. Provided that
u
0
∈
H
1
(
R
)
,
y
0
=
(
1
−
∂
x
2
)
u
0
∈
M
(
R
)
,
supp
y
0
−
⊂
(
−
∞
,
x
0
)
and
supp
y
0
+
⊂
(
x
0
,
∞
)
, the existence and uniqueness of global weak solutions for the equation are shown to be true in the space
W
l
o
c
1
,
∞
(
R
+
×
R
)
∩
L
l
o
c
∞
(
R
+
;
H
1
(
R
)
)
.</description><identifier>ISSN: 0362-546X</identifier><identifier>EISSN: 1873-5215</identifier><identifier>DOI: 10.1016/j.na.2011.04.051</identifier><identifier>CODEN: NOANDD</identifier><language>eng</language><publisher>Amsterdam: Elsevier Ltd</publisher><subject>Dissipation ; Exact sciences and technology ; Existence ; Global weak solution ; Mathematical analysis ; Mathematics ; Nonlinearity ; Sciences and techniques of general use ; The weakly dissipative Degasperis–Procesi equation ; Uniqueness</subject><ispartof>Nonlinear analysis, 2011-10, Vol.74 (15), p.4961-4973</ispartof><rights>2011 Elsevier Ltd</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c356t-b285a46ad34feb160780e99ef00e30477367907855aaff2d2b1651bdb8cfeac33</citedby><cites>FETCH-LOGICAL-c356t-b285a46ad34feb160780e99ef00e30477367907855aaff2d2b1651bdb8cfeac33</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.na.2011.04.051$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=24285285$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Guo, Yunxi</creatorcontrib><creatorcontrib>Lai, Shaoyong</creatorcontrib><creatorcontrib>Wang, Ying</creatorcontrib><title>Global weak solutions to the weakly dissipative Degasperis–Procesi equation</title><title>Nonlinear analysis</title><description>The global weak solutions for the Degasperis–Procesi equation with weakly dissipative term are investigated. Provided that
u
0
∈
H
1
(
R
)
,
y
0
=
(
1
−
∂
x
2
)
u
0
∈
M
(
R
)
,
supp
y
0
−
⊂
(
−
∞
,
x
0
)
and
supp
y
0
+
⊂
(
x
0
,
∞
)
, the existence and uniqueness of global weak solutions for the equation are shown to be true in the space
W
l
o
c
1
,
∞
(
R
+
×
R
)
∩
L
l
o
c
∞
(
R
+
;
H
1
(
R
)
)
.</description><subject>Dissipation</subject><subject>Exact sciences and technology</subject><subject>Existence</subject><subject>Global weak solution</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Nonlinearity</subject><subject>Sciences and techniques of general use</subject><subject>The weakly dissipative Degasperis–Procesi equation</subject><subject>Uniqueness</subject><issn>0362-546X</issn><issn>1873-5215</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp1kM9KxEAMxgdRcF29e-xFPLVm2k7b9Sb-B0UPCt6GdJrqrN3OOukq3nwH39AncdYVb0IgEH7fl-QTYldCIkEWB9OkxyQFKRPIE1ByTYxkVWaxSqVaFyPIijRWefGwKbaYpwAgy6wYievzztXYRW-EzxG7bjFY13M0uGh4op9p9x41ltnOcbCvFJ3QI_KcvOWvj89b7wyxjehlgUvhtthosWPa-e1jcX92end8EV_dnF8eH13FJlPFENdppTAvsMnylmpZQFkBTSbUAlAGeRkuKydhqBRi26ZNGhgl66auTEtosmws9le-c-9eFsSDnlk21HXYk1uwrqpJnlYlFIGEFWm8Y_bU6rm3M_TvWoJeBqenuke9DE5DrkNwQbL3a45ssGs99sbyny4NzipU4A5XHIVPXy15zcZSb6ixnsygG2f_X_INmI2D3g</recordid><startdate>20111001</startdate><enddate>20111001</enddate><creator>Guo, Yunxi</creator><creator>Lai, Shaoyong</creator><creator>Wang, Ying</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20111001</creationdate><title>Global weak solutions to the weakly dissipative Degasperis–Procesi equation</title><author>Guo, Yunxi ; Lai, Shaoyong ; Wang, Ying</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c356t-b285a46ad34feb160780e99ef00e30477367907855aaff2d2b1651bdb8cfeac33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Dissipation</topic><topic>Exact sciences and technology</topic><topic>Existence</topic><topic>Global weak solution</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Nonlinearity</topic><topic>Sciences and techniques of general use</topic><topic>The weakly dissipative Degasperis–Procesi equation</topic><topic>Uniqueness</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Guo, Yunxi</creatorcontrib><creatorcontrib>Lai, Shaoyong</creatorcontrib><creatorcontrib>Wang, Ying</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Nonlinear analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Guo, Yunxi</au><au>Lai, Shaoyong</au><au>Wang, Ying</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Global weak solutions to the weakly dissipative Degasperis–Procesi equation</atitle><jtitle>Nonlinear analysis</jtitle><date>2011-10-01</date><risdate>2011</risdate><volume>74</volume><issue>15</issue><spage>4961</spage><epage>4973</epage><pages>4961-4973</pages><issn>0362-546X</issn><eissn>1873-5215</eissn><coden>NOANDD</coden><abstract>The global weak solutions for the Degasperis–Procesi equation with weakly dissipative term are investigated. Provided that
u
0
∈
H
1
(
R
)
,
y
0
=
(
1
−
∂
x
2
)
u
0
∈
M
(
R
)
,
supp
y
0
−
⊂
(
−
∞
,
x
0
)
and
supp
y
0
+
⊂
(
x
0
,
∞
)
, the existence and uniqueness of global weak solutions for the equation are shown to be true in the space
W
l
o
c
1
,
∞
(
R
+
×
R
)
∩
L
l
o
c
∞
(
R
+
;
H
1
(
R
)
)
.</abstract><cop>Amsterdam</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.na.2011.04.051</doi><tpages>13</tpages></addata></record> |
| fulltext | fulltext |
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| ispartof | Nonlinear analysis, 2011-10, Vol.74 (15), p.4961-4973 |
| issn | 0362-546X 1873-5215 |
| language | eng |
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| source | Elsevier ScienceDirect Journals Complete |
| subjects | Dissipation Exact sciences and technology Existence Global weak solution Mathematical analysis Mathematics Nonlinearity Sciences and techniques of general use The weakly dissipative Degasperis–Procesi equation Uniqueness |
| title | Global weak solutions to the weakly dissipative Degasperis–Procesi equation |
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