On the Study of Global Solutions for a Nonlinear Equation

Haibo Yan and Ls Yong

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: 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).

Date: 2014
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https://doi.org/10.1155/2014/808214

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:808214

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