Existence and General Energy Decay of Solutions to a Coupled System of Quasi-Linear Viscoelastic Variable Coefficient Wave Equations with Nonlinear Source Terms
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作者:
Wang, Chengqiang
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机构:
Chengdu Normal Univ, Sch Math, Chengdu 611130, Peoples R China
Suqian Univ, Sch Math, Suqian 223800, Peoples R ChinaChengdu Normal Univ, Sch Math, Chengdu 611130, Peoples R China
Wang, Chengqiang
[1
,2
]
Wang, Can
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机构:
Chengdu Normal Univ, Sch Math, Chengdu 611130, Peoples R ChinaChengdu Normal Univ, Sch Math, Chengdu 611130, Peoples R China
Wang, Can
[1
]
Zhao, Xiangqing
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机构:
Suqian Univ, Sch Math, Suqian 223800, Peoples R ChinaChengdu Normal Univ, Sch Math, Chengdu 611130, Peoples R China
Zhao, Xiangqing
[2
]
Lv, Zhiwei
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h-index: 0
机构:
Suqian Univ, Sch Math, Suqian 223800, Peoples R ChinaChengdu Normal Univ, Sch Math, Chengdu 611130, Peoples R China
Lv, Zhiwei
[2
]
机构:
[1] Chengdu Normal Univ, Sch Math, Chengdu 611130, Peoples R China
[2] Suqian Univ, Sch Math, Suqian 223800, Peoples R China
existence results;
general energy decay;
quasi-linear wave equations;
variable coefficient wave equations;
viscoelastic damping;
UNIFORM DECAY;
BEHAVIOR;
RATES;
D O I:
10.3390/axioms12080780
中图分类号:
O29 [应用数学];
学科分类号:
070104 ;
摘要:
Viscoelastic damping phenomena are ubiquitous in diverse kinds of wave motions of nonlinear media. This arouses extensive interest in studying the existence, the finite time blow-up phenomenon and various large time behaviors of solutions to viscoelastic wave equations. In this paper, we are concerned with a class of variable coefficient coupled quasi-linear wave equations damped by viscoelasticity with a long-term memory fading at very general rates and possibly damped by friction but provoked by nonlinear interactions. We prove a local existence result for solutions to our concerned coupled model equations by applying the celebrated Faedo-Galerkin scheme. Based on the newly obtained local existence result, we prove that solutions would exist globally in time whenever their initial data satisfy certain conditions. In the end, we provide a criterion to guarantee that some of the global-in-time-existing solutions achieve energy decay at general rates uniquely determined by the fading rates of the memory. Compared with the existing results in the literature, our concerned model coupled wave equations are more general, and therefore our theoretical results have wider applicability. Modified energy functionals (can also be viewed as certain Lyapunov functionals) play key roles in proving our claimed general energy decay result in this paper.
机构:King Fahd Univ Petr & Minerals, Dept Math Sci, Dhahran 31261, Saudi Arabia
Berrimi, S
Messaoudi, SA
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机构:
King Fahd Univ Petr & Minerals, Dept Math Sci, Dhahran 31261, Saudi ArabiaKing Fahd Univ Petr & Minerals, Dept Math Sci, Dhahran 31261, Saudi Arabia
机构:King Fahd Univ Petr & Minerals, Dept Math Sci, Dhahran 31261, Saudi Arabia
Berrimi, S
Messaoudi, SA
论文数: 0引用数: 0
h-index: 0
机构:
King Fahd Univ Petr & Minerals, Dept Math Sci, Dhahran 31261, Saudi ArabiaKing Fahd Univ Petr & Minerals, Dept Math Sci, Dhahran 31261, Saudi Arabia