The Local Strong and Weak Solutions for a Generalized Novikov Equation
The Kato theorem for abstract differential equations is applied to establish the local well-posedness of the strong solution for a nonlinear generalized Novikov equation in space C([0,T),Hs(R))∩C1([0,T),Hs-1(R)) with s>(3/2). The existence of weak solutions for the equation in lower-order Sobolev...
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| Format: | Article |
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Hindawi Limited
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/158126 |
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doaj-35b4c4e56ada4759a24c48b0fd86607a2020-11-24T23:21:14ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/158126158126The Local Strong and Weak Solutions for a Generalized Novikov EquationMeng Wu0Yue Zhong1Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, ChinaDepartment of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, ChinaThe Kato theorem for abstract differential equations is applied to establish the local well-posedness of the strong solution for a nonlinear generalized Novikov equation in space C([0,T),Hs(R))∩C1([0,T),Hs-1(R)) with s>(3/2). The existence of weak solutions for the equation in lower-order Sobolev space Hs(R) with 1≤s≤(3/2) is acquired.http://dx.doi.org/10.1155/2012/158126 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Meng Wu Yue Zhong |
| spellingShingle |
Meng Wu Yue Zhong The Local Strong and Weak Solutions for a Generalized Novikov Equation Abstract and Applied Analysis |
| author_facet |
Meng Wu Yue Zhong |
| author_sort |
Meng Wu |
| title |
The Local Strong and Weak Solutions for a Generalized Novikov Equation |
| title_short |
The Local Strong and Weak Solutions for a Generalized Novikov Equation |
| title_full |
The Local Strong and Weak Solutions for a Generalized Novikov Equation |
| title_fullStr |
The Local Strong and Weak Solutions for a Generalized Novikov Equation |
| title_full_unstemmed |
The Local Strong and Weak Solutions for a Generalized Novikov Equation |
| title_sort |
local strong and weak solutions for a generalized novikov equation |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2012-01-01 |
| description |
The Kato theorem for abstract differential equations is applied to establish the local well-posedness of the strong solution for a nonlinear generalized Novikov equation in space C([0,T),Hs(R))∩C1([0,T),Hs-1(R)) with s>(3/2). The existence of weak solutions for the equation in lower-order Sobolev space Hs(R) with 1≤s≤(3/2) is acquired. |
| url |
http://dx.doi.org/10.1155/2012/158126 |
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