Volume 26, 2020
|Number of page(s)||26|
|Published online||17 July 2020|
A non-homogeneous boundary value problem for the Kuramoto-Sivashinsky equation posed in a finite interval*
School of Economics and Mathematics, Southwestern University of Finance and Economics,
2 Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221, USA.
3 School of Mathematics, Sichuan University, Chengdu 610064, China.
** Corresponding author: email@example.com
Accepted: 23 April 2019
This paper studies the initial boundary value problem (IBVP) for the dispersive Kuramoto-Sivashinsky equation posed in a finite interval (0, L) with non-homogeneous boundary conditions. It is shown that the IBVP is globally well-posed in the space Hs(0, L) for any s > −2 with the initial data in Hs(0, L) and the boundary value data belonging to some appropriate spaces. In addition, the IBVP is demonstrated to be ill-posed in the space Hs(0, L) for any s < −2 in the sense that the corresponding solution map fails to be in C2.
Mathematics Subject Classification: 35A01 / 35C15 / 35D30 / 35K20 / 35K55
Key words: Kuramoto-Sivashinsky equation / initial boundary value problem / well-posedness
© EDP Sciences, SMAI 2020
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