Stability for semilinear hyperbolic coupled system with frictional and viscoelastic localized damping

被引：12
|
作者：
Cavalcanti, M. M. [1 ]
Cavalcanti, V. N. Domingos [1 ]
Martinez, V. H. Gonzalez [1 ]
Peralta, V. A. [2 ]
Vicente, A. [3 ]
机构：
[1] Univ Estadual Maringa, Dept Math, BR-87020900 Maringa, Parana, Brazil
[2] Univ Tecnol Fed Parana, Dept Math, BR-86300000 Cornelio Procopio, PR, Brazil
[3] Western Parana State Univ, Ctr Exact & Technol Sci, Cascavel, PR, Brazil
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2020年 / 269卷 / 10期
关键词：
Stability; Semilinear hyperbolic coupled system; Localized frictional damping; Localized viscoelastic damping; Unique continuation principle for systems; OPTIMAL DECAY-RATES; WAVE-EQUATION; ASYMPTOTIC STABILITY; ENERGY DECAY; EXACT CONTROLLABILITY; GLOBAL ATTRACTORS; CRITICAL EXPONENT; WELL-POSEDNESS; GENERAL DECAY; BOUNDARY;
D O I：
10.1016/j.jde.2020.06.013
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we prove stability results for a semilinear hyperbolic coupled system subject to a viscoelastic localized damping acting in the first equation and a frictional localized one acting in the second equation of the system. We divide the proof into two parts. In the first part the equations are posed in a homogeneous medium Q with the damping acting in a boundary neighbourhood. In the second part the equations posed in an inhomogeneous medium Q with the damping acting in a collar of the boundary and in an appropriate mesh in the interior. Due to the assumptions on the nonlinear function involving the frictional damping, general decay rates are obtained. To prove the results we used the tools of the Microlocal Analysis Theory. (c) 2020 Elsevier Inc. All rights reserved.
引用
收藏
页码：8212 / 8268
页数：57
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