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

IF 1 4区数学 Q1 MATHEMATICS

Boundary Value Problems Pub Date : 2023-09-19 DOI:10.1186/s13661-023-01781-8

Billel Gheraibia, Nouri Boumaza

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引用次数: 0

Abstract

Abstract 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 $g'(t)\leq -\xi (t)g^{r}(t)$ g ′ ( t ) ≤ − ξ ( t ) g r ( t ) , $t\geq 0$ t ≥ 0 , $1\leq r< \frac{3}{2}$ 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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具有Balakrishnan-Taylor阻尼和时滞项的粘弹性波动方程的初边值问题:衰减估计和爆破结果

摘要本文研究了具有Balakrishnan-Taylor阻尼且松弛函数满足$g'(t)\leq -\xi (t)g^{r}(t)$ g ' (t)≤- ξ (t) g r (t)， $t\geq 0$ t≥0,$1\leq r< \frac{3}{2}$ 1≤r ＆lt的时滞项的粘弹性波动方程的初边值问题;3 .答案:b。本工作的主要目的是研究整体存在性、一般衰变和爆炸结果。通过引入合适的能量和李雅普诺夫泛函，建立了能量解的衰减性，并得到了初始能量为负的爆破结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Boundary Value Problems 数学-数学

自引率

5.90%

发文量

审稿时长

3 months

期刊介绍： The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.