Initial boundary value problem for a viscoelastic wave equation with Balakrishnan-Taylor damping and a delay term: decay estimates and blow-up result

被引：0
|
作者：
Gheraibia, Billel [1 ]
Boumaza, Nouri [2 ]
机构：
[1] Univ Oum El Bouaghi, Dept Math & Comp Sci, Oum El Bouaghi, Algeria
[2] Echahid Cheikh Larbi Tebessi Univ, Dept Math & Comp Sci, Tebessa, Algeria
来源：
BOUNDARY VALUE PROBLEMS | 2023年 / 2023卷 / 01期
关键词：
Wave equation; Balakrishnan-Taylor damping; Delay term; Global existence; Decay estimates; Blow up; GLOBAL EXISTENCE; ASYMPTOTIC STABILITY; ENERGY SOLUTIONS; KIRCHHOFF-TYPE; GENERAL DECAY;
D O I：
10.1186/s13661-023-01781-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the initial boundary value problem for the following viscoelastic wave equation with Balakrishnan-Taylor damping and a delay term where the relaxation function satisfies g'(t) <= -xi(t)g(r)(t), t >= 0, 1 <= r < 3/2. The main goal of this work is to study the global existence, general decay, and blow-up result. The global existence has been obtained by potential-well theory, the decay of solutions of energy has been established by introducing suitable energy and Lyapunov functionals, and a blow-up result has been obtained with negative initial energy.
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页数：17
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