具有时变过阻尼的三维双极欧拉-泊松系统平面扩散波的稳定性

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED Mathematical Methods in the Applied Sciences Pub Date : 2024-10-24 DOI:10.1002/mma.10560

Qiwei Wu, Xiaofeng Hou

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引用次数: 0

摘要

本文研究了具有时变过阻尼的三维双极欧拉-泊松系统Cauchy问题解的渐近性质。我们证明了在初始扰动足够小的情况下，柯西问题存在唯一的随时间趋于无穷远时趋于平面扩散波的全局时光滑解。此外，我们还得到了解对平面扩散波的收敛速率。用时间加权能量法完成了证明。

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Stability of planar diffusion wave for three-dimensional bipolar Euler–Poisson system with time-dependent over-damping

This paper is concerned with the asymptotic behavior of the solution to the Cauchy problem for the three-dimensional bipolar Euler–Poisson system with time-dependent over-damping. We prove that the Cauchy problem admits a unique global-in-time smooth solution that tends to the planar diffusion wave as time goes to infinity provided that the initial perturbation is sufficiently small. Moreover, we also obtain the convergence rate of the solution toward the planar diffusion wave. The proof is completed by the time-weighted energy method.

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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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