A nonhomogeneous boundary value problem for the Kuramoto–Sivashinsky equation in a quarter plane |
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| Authors: | Jing Li Bing‐Yu Zhang Zhixiong Zhang |
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| Institution: | 1. School of Economics and Mathematics, Southwestern University of Finance and Economics, Chengdu, China;2. Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH, USA;3. School of Mathematics, Sichuan University, China |
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| Abstract: | We study the initial boundary value problem for the one‐dimensional Kuramoto–Sivashinsky equation posed in a half line  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  , the initial boundary value problem of the Kuramoto–Sivashinsky equation is shown to be globally well‐posed in Sobolev space  for any s >?2. Copyright © 2017 John Wiley & Sons, Ltd. |
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| Keywords: | Kuramoto– Sivashinsky equation initial boundary value problem well‐posedness |
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