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

页码：6140 / 6164

页数：25

共 50 条

[31] Global existence and blow-up of solutions for p-Laplacian evolution equation with nonlinear memory term and nonlocal boundary condition
Fang, Zhong Bo
Zhang, Jianyun
BOUNDARY VALUE PROBLEMS, 2014,
[32] Global existence and energy decay of solutions to a viscoelastic Timoshenko beam system with a nonlinear delay term
Djilali, Laid
Benaissa, Abbes
Benaissa, Abdelkader
APPLICABLE ANALYSIS, 2016, 95 (12) : 2637 - 2660
[33] Global Solutions for a Nonlocal Problem with Logarithmic Source Term
Lapa, Eugenio Cabanillas
SAHAND COMMUNICATIONS IN MATHEMATICAL ANALYSIS, 2024, 21 (03): : 371 - 385
[34] Existence for a Singular Nonlocal Phase Field System with Inertial Term
Kurima, Shunsuke
ACTA APPLICANDAE MATHEMATICAE, 2022, 178 (01)
[35] General Energy Decay of Solutions for a Wave Equation with Nonlocal Damping and Nonlinear Boundary Damping
Li Donghao
Zhang Hongwei
Hu Qingying
JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS, 2019, 32 (04): : 369 - 380
[36] Existence for a Singular Nonlocal Phase Field System with Inertial Term
Shunsuke Kurima
Acta Applicandae Mathematicae, 2022, 178
[37] General decay of solutions to a viscoelastic wave equation with linear damping, nonlinear damping and source term
Li Qian
He Luofei
APPLICABLE ANALYSIS, 2020, 99 (07) : 1248 - 1259
[38] Global existence and boundedness in a chemotaxis model with singular sensitivity and nonlocal term
Du, Wenping
Liu, Suying
Zhang, Wenji
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2024, 75 (05):
[39] Uniform energy decay rates for nonlinear viscoelastic wave equation with nonlocal boundary damping
Li, Fushan
Zhao, Cuiling
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (11) : 3468 - 3477
[40] Blow-up of solutions for nonlinear parabolic equation with nonlocal source and nonlocal boundary condition
Cui, Zhoujin
Yang, Zuodong
Zhang, Rui
APPLIED MATHEMATICS AND COMPUTATION, 2013, 224 : 1 - 8

← 1 2 3 4 5 →