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arXiv · 1607.00506

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

Jing Li·Bing-Yu Zhang·Zhixiong Zhang
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Abstract

We study the initial boundary value problem for one-dimensional Kuramoto-Sivashinsky equation with nonhomogeneous boundary conditions. Through the analysis of the boundary integral operator, and applying the known results on the Cauchy problem, we obtain both the local well-posedness and the global well-posedness for the nonhomogeneous initial boundary value problem. It is shown that the Kuramoto-Sivashinsky equation is well-posed in Sobolev space $C([0,T]; H^s (R^+)) \bigcap L^2(0,T; H^{s+2}(R^+))$ for $s>-2$.

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Jing Li, Bing-Yu Zhang, Zhixiong Zhang. 2016-07-14. A nonhomogeneous boundary value problem for the Kuramoto-Sivashinsky equation in a quarter plane. https://doi.org/10.1002/mma.4413

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