Global attractors of the degenerate fractional Kirchhoff wave equation with structural damping or strong damping

IF 3.2 1区数学 Q1 MATHEMATICS

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI:10.1515/anona-2022-0226

Wenhua Yang, Jun Zhou

引用次数: 6

Abstract

Abstract This article deals with the degenerate fractional Kirchhoff wave equation with structural damping or strong damping. The well-posedness and the existence of global attractor in the natural energy space by virtue of the Faedo-Galerkin method and energy estimates are proved. It is worth mentioning that the results of this article cover the case of possible degeneration (or even negativity) of the stiffness coefficient. Moreover, under further suitable assumptions, the fractal dimension of the global attractor is shown to be infinite by using Z 2 {{\mathbb{Z}}}_{2} index theory.

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具有结构阻尼或强阻尼的退化分数Kirchhoff波动方程的全局吸引子

本文讨论了具有结构阻尼或强阻尼的退化分数阶基尔霍夫波动方程。利用Faedo-Galerkin方法和能量估计，证明了自然能量空间中全局吸引子的适定性和存在性。值得一提的是，本文的结果涵盖了刚度系数可能退化（甚至为负）的情况。此外，在进一步适当的假设下，通过使用Z2｛\mathbb｛Z｝｝}_｛2｝指数理论，证明了全局吸引子的分形维数是无限的。

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

Advances in Nonlinear Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

6.00

自引率

9.50%

发文量

审稿时长

30 weeks

期刊介绍： Advances in Nonlinear Analysis (ANONA) aims to publish selected research contributions devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The Journal focuses on papers that address significant problems in pure and applied nonlinear analysis. ANONA seeks to present the most significant advances in this field to a wide readership, including researchers and graduate students in mathematics, physics, and engineering.