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.

引用

页数：17

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