On the Study of Global Solutions for a Nonlinear Equation
The well-posedness of global strong solutions for a nonlinear partial differential equation including the Novikov equation is established provided that its initial value v0(x) satisfies a sign condition and v0(x)∈Hs(R) with s>3/2. If the initial value v0(x)∈Hs(R) (1≤s≤3/2) and the mean function...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/808214 |
| Summary: | The well-posedness of global strong solutions for a nonlinear partial differential equation including the Novikov equation is established provided that its initial value v0(x) satisfies a sign condition and v0(x)∈Hs(R) with s>3/2. If the initial value v0(x)∈Hs(R) (1≤s≤3/2) and the mean function of (1-∂x2)v0(x) satisfies the sign condition, it is proved that there exists at least one global weak solution to the equation in the space v(t,x)∈L2([0,+∞),Hs(R)) in the sense of distribution and vx∈L∞([0,+∞)×R). |
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| ISSN: | 1085-3375 1687-0409 |