Stabilization of a weak viscoelastic wave equation in Riemannian geometric setting with an interior delay under nonlinear boundary dissipation

被引:3
作者
Li, Sheng-Jie [1 ,2 ]
Chai, Shugen [1 ]
Lasiecka, Irena [2 ,3 ]
机构
[1] Shanxi Univ, Sch Math & Stat, Taiyuan 030006, Peoples R China
[2] Polish Acad Sci, IBS Syst Res Inst, Newelska 6, PL-01447 Warsaw, Poland
[3] Univ Memphis, Dept Math Sci, Memphis, TN 38152 USA
基金
中国国家自然科学基金;
关键词
Weak viscoelastic wave equation; Variable coefficient; Delay; Faedo-Galerkin method; Monotone operator theory; Riemannian geometry method; VARIABLE-COEFFICIENTS; GENERAL DECAY; UNIFORM DECAY; EXISTENCE; MEMORY; TERM;
D O I
10.1016/j.nonrwa.2024.104252
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The stabilization of a weak viscoelastic wave equation with variable coefficients in the principal part of elliptic operator and an interior delay is considered. The dynamics is subject to a nonlinear boundary dissipation. This leads to a non-dissipative dynamics. The existence of solution is demonstrated by means of Faedo-Galerkin method combined with monotone operator theory in handling nonlinear boundary conditions. The main result pertains to exponential decay rates for energy, which depend on the geometry of the spatial domain, viscoelastic effects, the strength of delay and the strength of mechanical boundary damping. An important feature of the model is the fact that the delay term and stabilizing mechanism are not collocated geometrically - in contrast with many other works on the subject. This aspect of the problem requires the appropriate tools in order to exhibit propagation of the dissipation from one location to another. The precise ranges of admissible parameters characterizing the model and ensuring the stability are provided. The methods of proofs are routed in Riemannian geometry.
引用
收藏
页数:28
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