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 H$$(0, L) for any s > −2 with the initial data in H$$(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 H$$(0, L) for any s < −2 in the sense that the corresponding solution map fails to be in C2.
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DOI : 10.1051/cocv/2019027
Mots-clés : Kuramoto-Sivashinsky equation, initial boundary value problem, well-posedness
@article{COCV_2020__26_1_A43_0,
author = {Li, Jing and Zhang, Bing-Yu and Zhang, Zhixiong},
title = {A non-homogeneous boundary value problem for the {Kuramoto-Sivashinsky} equation posed in a finite interval},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {26},
year = {2020},
doi = {10.1051/cocv/2019027},
zbl = {1446.35049},
mrnumber = {4124318},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2019027/}
}
TY - JOUR AU - Li, Jing AU - Zhang, Bing-Yu AU - Zhang, Zhixiong TI - A non-homogeneous boundary value problem for the Kuramoto-Sivashinsky equation posed in a finite interval JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2019027/ DO - 10.1051/cocv/2019027 LA - en ID - COCV_2020__26_1_A43_0 ER -
%0 Journal Article %A Li, Jing %A Zhang, Bing-Yu %A Zhang, Zhixiong %T A non-homogeneous boundary value problem for the Kuramoto-Sivashinsky equation posed in a finite interval %J ESAIM: Control, Optimisation and Calculus of Variations %D 2020 %V 26 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2019027/ %R 10.1051/cocv/2019027 %G en %F COCV_2020__26_1_A43_0
Li, Jing; Zhang, Bing-Yu; Zhang, Zhixiong. A non-homogeneous boundary value problem for the Kuramoto-Sivashinsky equation posed in a finite interval. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 43. doi : 10.1051/cocv/2019027. http://archive.numdam.org/articles/10.1051/cocv/2019027/
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Cité par Sources :
This work was partially supported by the National Natural Science Foundation of China (No. 11301425, No. 11571244 and No. 11231007) and the PCSIRT of the Ministry of Education of China under grant IRT 16R53.
