Global Existence and Stability for a Viscoelastic Wave Equation with Nonlinear Boundary Source Term

被引：0

作者：

Mohamed, Mellah ^{[1
]}

Ali, Hakem ^{[1
]}

Gongwei, Liu ^{[2
]}

机构：

[1] Univ Djillali Liabes Sidi Bel Abbes, Lab ACEDP, Sidi Bel Abbes 22000, Algeria

[2] Henan Univ Technol, Coll Sci, Zhengzhou 450001, Peoples R China

来源：

JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS | 2024年 / 37卷 / 04期

关键词：

Viscoelastic equation; nonlinear boundary source; stabilization; GENERAL DECAY; BLOW-UP; NONEXISTENCE; ENERGY;

D O I：

10.4208/jpde.v37.n4.6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work considers the initial boundary value problem for a viscoelastic wave equation with a nonlinear boundary source term. Under suitable assumptions, we prove the existence of global weak solutions using the Galerkin approximation. Then, we give a decay rate estimate of the energy by making use of the perturbed energy method.

引用

页码：467 / 481

页数：15

共 50 条

[1] Global existence and nonexistence of solutions for a viscoelastic wave equation with nonlinear boundary source term
Di, Huafei
Shang, Yadong
Peng, Xiaoming
MATHEMATISCHE NACHRICHTEN, 2016, 289 (11-12) : 1408 - 1432
[2] GLOBAL EXISTENCE AND NONEXISTENCE FOR THE VISCOELASTIC WAVE EQUATION WITH NONLINEAR BOUNDARY DAMPING-SOURCE INTERACTION
Said-Houari, Belkacem
Falcao Nascimento, Flavio A.
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2013, 12 (01) : 375 - 403
[3] Existence and exponential stability for the wave equation with nonlinear interior source and localized viscoelastic boundary feedback
Faria, Josiane Cristina de Oliveira
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2024, (47) : 1 - 18
[4] ON VISCOELASTIC WAVE EQUATION WITH NONLINEAR BOUNDARY DAMPING AND SOURCE TERM
Ha, Tae Gab
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2010, 9 (06) : 1543 - 1576
[5] Global existence, nonexistence, and decay of solutions for a viscoelastic wave equation with nonlinear boundary damping and source terms
Yu, Jiali
Shang, Yadong
Di, Huafei
JOURNAL OF MATHEMATICAL PHYSICS, 2020, 61 (07)
[6] Stability of wave equation with locally viscoelastic damping and nonlinear boundary source
Hao, Jianghao
Lv, Mengxian
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2020, 490 (01)
[7] Global solvability and asymptotic stability for the wave equation with nonlinear boundary damping and source term
Cavalcanti, MM
Cavalcanti, VND
Soriano, JA
CONTRIBUTIONS TO NONLINEAR ANALYSIS: A TRIBUTE TO D. G. DE FIGUEIREDO ON THE OCCASION OF HIS 70TH BIRTHDAY, 2006, 66 : 161 - +
[8] Global existence for the wave equation with nonlinear boundary damping and source terms
Vitillaro, E
JOURNAL OF DIFFERENTIAL EQUATIONS, 2002, 186 (01) : 259 - 298
[9] On a viscoelastic equation with nonlinear boundary damping and source terms: Global existence and decay of the solution
Lu, Liqing
Li, Shengjia
Chai, Shugen
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2011, 12 (01) : 295 - 303
[10] Global existence uniqueness and decay estimates for nonlinear viscoelastic wave equation with boundary dissipation
Li, Fushan
Zhao, Zengqin
Chen, Yanfu
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2011, 12 (03) : 1759 - 1773

← 1 2 3 4 5 →