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;
D O I：
暂无
中图分类号：
学科分类号：
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.
引用
收藏
相关论文
共 128 条
[21]  
Biagioni HA(2000)Global stabilization of the Kuramoto-Sivashinsky equation via distributed output feedback control Syst. Control Lett. 39 283-437
[22]  
Bona JL(2016)A singular limit problem for the Rosenau-Korteweg-de Vries-regularized long wave and Rosenau-regularized long wave equations Adv. Nonlinear Stud. 16 421-540
[23]  
Iorio RJ(2017)A Lyapunov functional for a system with both lumped and distributed delay Arch. Control Sci. 27 527-147
[24]  
Scialom M(2015)A new global Carleman estimate for the one-dimensional Kuramoto-Sivashinsky equation and applications to exact controllability to the trajectories and an inverse problem Nonlinear Anal. 117 133-296
[25]  
Biagioni HA(2015)Null controllability with constraints on the state for the 1-D Kuramoto-Sivashinsky equation Evol. Equ. Control Theory 4 281-19
[26]  
Gramchev T(2020)Global exact controllability of the trajectoris of the Kuramoto-Sivashinsky equation Evol. Equ. Control Theory 9 181-799
[27]  
Cazacu CM(2018)Stabilization of nonlinear rotating disk-beam system with localized thermal effect Nonlinear Dyn. 93 785-318
[28]  
Ignat LI(2005)New bounds for the Kuramoto-Sivashinsky equation Comm. Pure Appl. Math. 58 297-2265
[29]  
Pazoto AF(2015)New bounds for the inhomogenous Burgers and the Kuramoto-Sivashinsky equations Comm. Partial Differ. Equ. 40 2237-194
[30]  
Cerpa E(2017)Stabilizing nontrivial solutions of the generalized Kuramoto-Sivashinsky equation using feedback and optimal control IMA J. Appl. Math. 82 158-306
12345678910