关于一类耦合非线性粘弹性基尔霍夫方程变指数：解的全局存在性、爆炸、增长和衰减

IF 1.7 4区数学 Q1 Mathematics

Boundary Value Problems Pub Date : 2024-05-10 DOI:10.1186/s13661-024-01864-0

Abdelbaki Choucha, Mohamed Haiour, Salah Boulaaras

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引用次数: 0

摘要

在这项研究中，我们考虑了一个具有分散、源和可变指数的粘弹性准线性方程组。在初始数据和松弛函数的适当假设下，我们得到了该系统的解是全局和有界的。接着，证明了负初始能量下的炸毁。之后，利用正初始能量证明了解的指数增长，并通过使用 Komornik 提出的积分不等式，得到了无源项情况下的一般衰减结果。

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On a class of a coupled nonlinear viscoelastic Kirchhoff equations variable-exponents: global existence, blow up, growth and decay of solutions

In this work, we consider a quasilinear system of viscoelastic equations with dispersion, source, and variable exponents. Under suitable assumptions on the initial data and the relaxation functions, we obtained that the solution of the system is global and bounded. Next, the blow-up is proved with negative initial energy. After that, the exponential growth of solutions is showed with positive initial energy, and by using an integral inequality due to Komornik, the general decay result is obtained in the case of absence of the source term.

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来源期刊

Boundary Value Problems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.00

自引率

5.90%

发文量

审稿时长

4 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.