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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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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 |
| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |