The asymptotic behaviors of solutions for higher-order (m1, m2)-coupled Kirchhoff models with nonlinear strong damping

IF 2 3区数学 Q1 MATHEMATICS

Demonstratio Mathematica Pub Date : 2023-01-01 DOI:10.1515/dema-2022-0197

Penghui Lv, Guoguang Lin, Xiaojun Lv

引用次数: 3

Abstract

Abstract The Kirchhoff model is derived from the vibration problem of stretchable strings. This article focuses on the long-time dynamics of a class of higher-order coupled Kirchhoff systems with nonlinear strong damping. The existence and uniqueness of the solutions of these equations in different spaces are proved by prior estimation and the Faedo-Galerkin method. Subsequently, the family of global attractors of these problems is proved using the compactness theorem. In this article, we systematically propose the definition and proof process of the family of global attractors and enrich the related conclusions of higher-order coupled Kirchhoff models. The conclusions lay a theoretical foundation for future practical applications.

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具有非线性强阻尼的高阶(m1, m2)耦合Kirchhoff模型解的渐近行为

摘要Kirchhoff模型是从可拉伸弦的振动问题导出的。本文研究了一类具有非线性强阻尼的高阶耦合Kirchhoff系统的长时间动力学。用先验估计和Faedo-Galerkin方法证明了这些方程在不同空间中解的存在性和唯一性。随后，利用紧致性定理证明了这些问题的全局吸引子族。本文系统地提出了全局吸引子族的定义和证明过程，丰富了高阶耦合Kirchhoff模型的相关结论。这些结论为今后的实际应用奠定了理论基础。

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

Demonstratio Mathematica MATHEMATICS-

CiteScore

2.40

自引率

5.00%

发文量

审稿时长

35 weeks

期刊介绍： Demonstratio Mathematica publishes original and significant research on topics related to functional analysis and approximation theory. Please note that submissions related to other areas of mathematical research will no longer be accepted by the journal. The potential topics include (but are not limited to): -Approximation theory and iteration methods- Fixed point theory and methods of computing fixed points- Functional, ordinary and partial differential equations- Nonsmooth analysis, variational analysis and convex analysis- Optimization theory, variational inequalities and complementarity problems- For more detailed list of the potential topics please refer to Instruction for Authors. The journal considers submissions of different types of articles. "Research Articles" are focused on fundamental theoretical aspects, as well as on significant applications in science, engineering etc. “Rapid Communications” are intended to present information of exceptional novelty and exciting results of significant interest to the readers. “Review articles” and “Commentaries”, which present the existing literature on the specific topic from new perspectives, are welcome as well.