Global well posedness and limit behavior of the solutions to the viscous Degasperis–Procesi equation
This paper is concerned with the global well posedness and limit behavior of the solutions to the viscous Degasperis–Procesi equation. We prove the global existence and uniqueness of solution to the viscous Degasperis–Procesi equation for u 0 ∊ L 2 ( R ) . The local well posedness for u 0 ∊ L 2 ( R...
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| Veröffentlicht in: | Journal of mathematical physics 2009-03, Vol.50 (3), p.033503-033503-16 |
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| container_end_page | 033503-16 |
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| container_issue | 3 |
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| container_title | Journal of mathematical physics |
| container_volume | 50 |
| creator | Tian, Lixin Liang, Shujuan |
| description | This paper is concerned with the global well posedness and limit behavior of the solutions to the viscous Degasperis–Procesi equation. We prove the global existence and uniqueness of solution to the viscous Degasperis–Procesi equation for
u
0
∊
L
2
(
R
)
. The local well posedness for
u
0
∊
L
2
(
R
)
has been proven based on the energy estimate. The strong and weak limit behaviors of solution to the viscous Degasperis–Procesi equation are obtained. |
| doi_str_mv | 10.1063/1.3077225 |
| format | Article |
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u
0
∊
L
2
(
R
)
. The local well posedness for
u
0
∊
L
2
(
R
)
has been proven based on the energy estimate. The strong and weak limit behaviors of solution to the viscous Degasperis–Procesi equation are obtained.</description><identifier>ISSN: 0022-2488</identifier><identifier>EISSN: 1089-7658</identifier><identifier>DOI: 10.1063/1.3077225</identifier><identifier>CODEN: JMAPAQ</identifier><language>eng</language><publisher>Melville, NY: American Institute of Physics</publisher><subject>Estimates ; Exact sciences and technology ; Mathematical methods in physics ; Mathematics ; Physics ; Sciences and techniques of general use ; Solutions</subject><ispartof>Journal of mathematical physics, 2009-03, Vol.50 (3), p.033503-033503-16</ispartof><rights>American Institute of Physics</rights><rights>2009 American Institute of Physics</rights><rights>2009 INIST-CNRS</rights><rights>Copyright American Institute of Physics Mar 2009</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c411t-1b09a1ca573198a758ca493096dbc56515f1e6cac8503b290968b649cf079be73</citedby><cites>FETCH-LOGICAL-c411t-1b09a1ca573198a758ca493096dbc56515f1e6cac8503b290968b649cf079be73</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://pubs.aip.org/jmp/article-lookup/doi/10.1063/1.3077225$$EHTML$$P50$$Gscitation$$H</linktohtml><link.rule.ids>314,778,782,792,1556,4500,27911,27912,76139,76145</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=21384378$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Tian, Lixin</creatorcontrib><creatorcontrib>Liang, Shujuan</creatorcontrib><title>Global well posedness and limit behavior of the solutions to the viscous Degasperis–Procesi equation</title><title>Journal of mathematical physics</title><description>This paper is concerned with the global well posedness and limit behavior of the solutions to the viscous Degasperis–Procesi equation. We prove the global existence and uniqueness of solution to the viscous Degasperis–Procesi equation for
u
0
∊
L
2
(
R
)
. The local well posedness for
u
0
∊
L
2
(
R
)
has been proven based on the energy estimate. The strong and weak limit behaviors of solution to the viscous Degasperis–Procesi equation are obtained.</description><subject>Estimates</subject><subject>Exact sciences and technology</subject><subject>Mathematical methods in physics</subject><subject>Mathematics</subject><subject>Physics</subject><subject>Sciences and techniques of general use</subject><subject>Solutions</subject><issn>0022-2488</issn><issn>1089-7658</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><recordid>eNqNkMtKxDAUQIMoOD4W_kEQXChUc5OmTTeCjE8QdKHrkGZSjdSm5rYj7vwH_9AvseOMulJcBW5OziWHkC1g-8AycQD7guU553KJjICpIskzqZbJiDHOE54qtUrWEB8YA1BpOiLVWR1KU9NnV9e0DegmjUOkppnQ2j_6jpbu3kx9iDRUtLt3FEPddz40SLvwOZh6tKFHeuzuDLYuenx_fbuOwTr01D31ZkZvkJXK1Og2F-c6uT09uRmfJ5dXZxfjo8vEpgBdAiUrDFgjcwGFMrlU1qSFYEU2Ka3MJMgKXGaNVZKJkhfDhSqztLAVy4vS5WKdbM-9bQxPvcNOP4Q-NsNKzUFmMIj5AO3OIRsDYnSVbqN_NPFFA9Ozihr0ouLA7iyEBq2pq2ga6_H7AQehUpGrgTucc2h99_nl36Xz5HqWXH8lHwR7_xb8BU9D_AF1O6nEB1nLpCw</recordid><startdate>20090301</startdate><enddate>20090301</enddate><creator>Tian, Lixin</creator><creator>Liang, Shujuan</creator><general>American Institute of Physics</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope></search><sort><creationdate>20090301</creationdate><title>Global well posedness and limit behavior of the solutions to the viscous Degasperis–Procesi equation</title><author>Tian, Lixin ; Liang, Shujuan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c411t-1b09a1ca573198a758ca493096dbc56515f1e6cac8503b290968b649cf079be73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Estimates</topic><topic>Exact sciences and technology</topic><topic>Mathematical methods in physics</topic><topic>Mathematics</topic><topic>Physics</topic><topic>Sciences and techniques of general use</topic><topic>Solutions</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Tian, Lixin</creatorcontrib><creatorcontrib>Liang, Shujuan</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Journal of mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Tian, Lixin</au><au>Liang, Shujuan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Global well posedness and limit behavior of the solutions to the viscous Degasperis–Procesi equation</atitle><jtitle>Journal of mathematical physics</jtitle><date>2009-03-01</date><risdate>2009</risdate><volume>50</volume><issue>3</issue><spage>033503</spage><epage>033503-16</epage><pages>033503-033503-16</pages><issn>0022-2488</issn><eissn>1089-7658</eissn><coden>JMAPAQ</coden><abstract>This paper is concerned with the global well posedness and limit behavior of the solutions to the viscous Degasperis–Procesi equation. We prove the global existence and uniqueness of solution to the viscous Degasperis–Procesi equation for
u
0
∊
L
2
(
R
)
. The local well posedness for
u
0
∊
L
2
(
R
)
has been proven based on the energy estimate. The strong and weak limit behaviors of solution to the viscous Degasperis–Procesi equation are obtained.</abstract><cop>Melville, NY</cop><pub>American Institute of Physics</pub><doi>10.1063/1.3077225</doi><tpages>16</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0022-2488 |
| ispartof | Journal of mathematical physics, 2009-03, Vol.50 (3), p.033503-033503-16 |
| issn | 0022-2488 1089-7658 |
| language | eng |
| recordid | cdi_pascalfrancis_primary_21384378 |
| source | AIP Journals Complete; AIP Digital Archive |
| subjects | Estimates Exact sciences and technology Mathematical methods in physics Mathematics Physics Sciences and techniques of general use Solutions |
| title | Global well posedness and limit behavior of the solutions to the viscous Degasperis–Procesi equation |
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