Global existence and decay of solutions of a singular nonlocal viscoelastic system with a nonlinear source term, nonlocal boundary condition, and localized damping term

被引：13
作者：
Boulaaras, Salah [1 ,2 ]
Mezouar, Nadia [3 ]
机构：
[1] Qassim Univ, Dept Math, Coll Sci & Arts, Al Rass, Saudi Arabia
[2] Univ Oran, Lab Fundamental & Appl Math Oran LMFAO, Oran, Algeria
[3] Mustapha Stambouli Univ, Fac Econ, Mascara, Algeria
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2020年 / 43卷 / 10期
关键词：
damping terms; general decay; global existence; viscoelastic equations; BLOW-UP; EQUATION;
D O I：
10.1002/mma.6361
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The paper deals with the existence of a global solution of a singular one-dimensional viscoelastic system with a nonlinear source term, nonlocal boundary condition, and localized frictional damping a(x)u(t) using the potential well theory. Furthermore, the general decay result is proved. We construct a suitable Lyapunov functional and make use of the perturbed energy method.
引用
收藏
页码：6140 / 6164
页数：25
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