科研之友
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摘要
We study the initial boundary value problem for the one-dimensional Kuramoto-Sivashinsky equation posed in a half line R+ with nonhomogeneous boundary conditions. Through the analysis of the boundary integral operator, and applying the known results of the Cauchy problem of the Kuramoto-Sivashinsky equation posed on the whole line R, the initial boundary value problem of the Kuramoto-Sivashinsky equation is shown to be globally well-posed in Sobolev space Hs(R+) for any s>-2.
