Uniform Stabilization for the Semi-linear Wave Equation with Nonlinear Kelvin-Voigt Damping

被引：0
|
作者：
Ammari, Kais [1 ]
Cavalcanti, Marcelo M. [2 ]
Mansouri, Sabeur [1 ]
机构：
[1] Univ Monastir, Fac Sci Monastir, Dept Math, LR 22ES03,LR Anal & Control PDEs, Monastir, Tunisia
[2] Univ Estadual Maringa, Dept Math, BR-87020900 Maringa, Parana, Brazil
来源：
APPLIED MATHEMATICS AND OPTIMIZATION | 2024年 / 90卷 / 02期
关键词：
Uniform stabilization; Semilinear wave equation; Nonlinear Kelvin-Voigt damping; Viscoelastic feedback; EXPONENTIAL DECAY; EXACT CONTROLLABILITY; ASYMPTOTIC STABILITY; ENERGY;
D O I：
10.1007/s00245-024-10186-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is concerned with the decay estimate of solutions to the semilinear wave equation subject to two localized dampings in a bounded domain. The first one is of the nonlinear Kelvin-Voigt type which is distributed around a neighborhood of the boundary and the second is a frictional damping depending in the first one. We show uniform decay rate results of the corresponding energy for all initial data taken in bounded sets of finite energy phase-space. The proof is based on obtaining an observability inequality which combines unique continuation properties and the tools of the Microlocal Analysis Theory
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页数：27
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