Well-posedness and exponential stability results for a nonlinear Kuramoto-Sivashinsky equation with a boundary time-delay

被引：0
作者：
Boumediène Chentouf
机构：
[1] Kuwait University,Department of Mathematics, Faculty of Science
来源：
Analysis and Mathematical Physics | 2021年 / 11卷
关键词：
Nonlinear Kuramoto-Sivashinsky equation; Boundary delay; Well-posedness; Exponential Stability;
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摘要：
The main concern of this article is to deal with the presence of a boundary delay in the nonlinear Kuramoto-Sivashinsky equation. First, we prove that the whole system is well-posed under a smallness assumption on the initial data and a condition on the parameter involved in the delay term. Then, the solution is shown to decay exponentially despite the presence of the delay. These findings are proved by considering several situations depending on the physical parameters of the system.
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