一类变指数非线性弱耗散粘弹性方程的稳定性结果:理论与数值

IF 1.9 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Mathematical & Computational Applications Pub Date : 2023-01-04 DOI:10.3390/mca28010005

A. Al‐Mahdi, M. Al‐Gharabli, Maher Noor, J. Audu

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引用次数: 0

摘要

本文研究了具有变指数非线性形式utt+Δ2u -∫0tg(t - s)Δu(s)ds+a|但|n(·)- 2ut - Δut=0的弱耗散粘弹性方程的长时间行为，其中n(.)是满足某些假设的连续函数，g是满足g ' (t)≤- ξ(t) g(g(t))的一般松弛函数，其中ξ和g是满足某些特定性质的函数，这些性质将在本文中提到。根据g的衰减率和变指数n(.)的性质，我们建立了能量泛函的显式和一般的衰减结果。我们给出了一些数值例子来支持我们的理论结果。我们的结果改进了文献中一些早期的工作。

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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Stability Results for a Weakly Dissipative Viscoelastic Equation with Variable-Exponent Nonlinearity: Theory and Numerics

In this paper, we study the long-time behavior of a weakly dissipative viscoelastic equation with variable exponent nonlinearity of the form utt+Δ2u−∫0tg(t−s)Δu(s)ds+a|ut|n(·)−2ut−Δut=0, where n(.) is a continuous function satisfying some assumptions and g is a general relaxation function such that g′(t)≤−ξ(t)G(g(t)), where ξ and G are functions satisfying some specific properties that will be mentioned in the paper. Depending on the nature of the decay rate of g and the variable exponent n(.), we establish explicit and general decay results of the energy functional. We give some numerical illustrations to support our theoretical results. Our results improve some earlier works in the literature.

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来源期刊

Mathematical & Computational Applications MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

自引率

10.50%

发文量

审稿时长

12 weeks

期刊介绍： Mathematical and Computational Applications (MCA) is devoted to original research in the field of engineering, natural sciences or social sciences where mathematical and/or computational techniques are necessary for solving specific problems. The aim of the journal is to provide a medium by which a wide range of experience can be exchanged among researchers from diverse fields such as engineering (electrical, mechanical, civil, industrial, aeronautical, nuclear etc.), natural sciences (physics, mathematics, chemistry, biology etc.) or social sciences (administrative sciences, economics, political sciences etc.). The papers may be theoretical where mathematics is used in a nontrivial way or computational or combination of both. Each paper submitted will be reviewed and only papers of highest quality that contain original ideas and research will be published. Papers containing only experimental techniques and abstract mathematics without any sign of application are discouraged.