Global and exponential attractors for viscoelastic Kirchhoff plate equation with memory and time delay

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED Mathematical Methods in the Applied Sciences Pub Date : 2024-09-18 DOI:10.1002/mma.10487

Yuming Qin, Hongli Wang

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Abstract

In this paper, we consider the viscoelastic Kirchhoff plate equation with memory and time delay. Under appropriate conditions on the real numbers $μ_{1}$ and $μ_{2}$ , we prove the existence of a compact global attractor with finite fractal dimension through a stabilizability estimate. Additionally, we demonstrate the existence of a fractal exponential attractor. To the best of our knowledge, these findings are novel for for this system.

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具有记忆和时间延迟的粘弹性基尔霍夫板方程的全局吸引子和指数吸引子

在本文中，我们考虑了具有记忆和时间延迟的粘弹性基尔霍夫板方程。在实数和的适当条件下，我们通过稳定度估计证明了有限分形维度的紧凑全局吸引子的存在。此外，我们还证明了分形指数吸引子的存在。据我们所知，这些发现对于该系统来说是新颖的。

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.

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