双流体欧拉-泊松系统的全局零振荡极限

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-04-12 DOI:10.1007/s00245-024-10131-8

Cunming Liu, Han Sheng

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引用次数: 0

摘要

我们研究了双流体欧拉-泊松系统的松弛问题。我们证明了系统在恒定平衡态附近光滑解的全局时间收敛性。当松弛时间趋近于零时，极限系统为双流体漂移扩散系统。在证明过程中，我们建立了所有参数和时间的平稳解的均匀能量估计。通过这些估计值，我们可以通过系统中的极限得到极限系统。此外，我们还通过流函数技术获得了解的全局收敛速率。

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Global Zero-Relaxation Limit for a Two-Fluid Euler–Poisson System

We study the relaxation problem for a two-fluid Euler-Poisson system. We prove the global-in-time convergence of the system for smooth solutions near the constant equilibrium states. The limit system is the two-fluid drift-diffusion system as the relaxation time tends to zero. In the proof, we establish uniform energy estimates of smooth solutions for all the parameters and the time. These estimates allow us to pass to the limit in the system to obtain the limit system. Moreover, the global convergence rate of the solutions is obtained by stream function techniques.

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.