A non-homogeneous boundary value problem for the Kuramoto-Sivashinsky equation posed in a finite interval*

被引：14

作者：

Li, Jing ^{[1
]}

Zhang, Bing-Yu ^{[2
]}

Zhang, Zhixiong ^{[3
]}

机构：

[1] Southwestern Univ Finance & Econ, Sch Econ & Math, Chengdu 611130, Peoples R China

[2] Univ Cincinnati, Dept Math Sci, Cincinnati, OH 45221 USA

[3] Sichuan Univ, Sch Math, Chengdu 610064, Peoples R China

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2020年 / 26卷 / 26期

基金：

中国国家自然科学基金;

关键词：

Kuramoto-Sivashinsky equation; initial boundary value problem; well-posedness; SHARP WELL-POSEDNESS; DE-VRIES EQUATION; INSTABILITY;

D O I：

10.1051/cocv/2019027

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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 spaceH(s)(0,L) for anys> -2 with the initial data inH(s)(0,L) and the boundary value data belonging to some appropriate spaces. In addition, the IBVP is demonstrated to be ill-posed in the spaceH(s)(0,L) for anys< -2 in the sense that the corresponding solution map fails to be inC(2).

引用

页数：26

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