Stabilization for the Klein-Gordon-Zakharov system

被引：0
|
作者：
Li, Weijia [1 ]
Shangguan, Yuqi [1 ]
Yan, Weiping [1 ]
机构：
[1] Guangxi Univ, Coll Math & Informat Sci, Nanning 530004, Peoples R China
来源：
ASYMPTOTIC ANALYSIS | 2023年 / 135卷 / 3-4期
基金：
中国国家自然科学基金;
关键词：
Stabilizability; quasi-periodic wave solutions; Klein-Gordon-Zakharov system; Kelvin-Voigt damping; WAVE-EQUATION; GLOBAL-SOLUTIONS; ENERGY SPACE; CONVERGENCE; EXISTENCE; CAUCHY;
D O I：
10.3233/ASY-231856
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper deals with global stability dynamics for the Klein-Gordon-Zakharov system in R-2. We first establish that this system admits a family of linear mode unstable explicit quasi-periodic wave solutions. Next, we prove that the Kelvin-Voigt damping can help to stabilize those linear mode unstable explicit quasi-periodic wave solutions for the Klein-Gordon-Zakharov system in the Sobolev space Hs+1(R-2) x Hs+1(R-2) x Hs+1(R-2) for any s >= 1. Moreover, the Kelvin-Voigt damped Klein-Gordon-Zakharov system admits a unique Sobolev regular solution exponentially convergent to some special solutions (including quasi-periodic wave solutions) of it. Our result can be extended to the n-dimension dissipative Klein-Gordon-Zakharov system for any n >= 1.
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页码：305 / 348
页数：44
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