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We study the initial boundary value problem for the one‐dimensional Kuramoto–Sivashinsky equation posed in a half lineR    +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 spaceH    s    (    R    +    )   for any  s >−2. Copyright © 2017 John Wiley & Sons, Ltd.

A nonhomogeneous boundary value problem for the Kuramoto–Sivashinsky equation in a quarter plane