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: firstname.lastname@example.org
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.