A Half-Space Problem on the Full Euler-Poisson System
A Half-Space Problem on the Full Euler-Poisson System
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DOI：
10.1137/20m1377084
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发表时间：
2020-11
期刊：
影响因子：
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通讯作者：
Renjun Duan;Haiyan Yin;Changjiang Zhu
中科院分区：
文献类型：
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作者：
Renjun Duan;Haiyan Yin;Changjiang Zhu
本文讨论半直线上离子的全Euler-Poisson系统的初边值问题。在类似于等熵情形的Bohm判据下，我们建立了平稳解的存在性，并进一步得到了在某些加权Sobolev空间中初始扰动足够小时，小幅度平稳解的大时间渐近稳定性。此外，还得到了解向定常解的收敛速度。证明是基于能量法的。一个关键点是捕捉时间能量耗散泛函和边界项的正性，根据输入的远场速度是否是临界的，用适当的代数权函数或指数空间权函数。
This paper is concerned with the initial-boundary value problem on the full Euler-Poisson system for ions over a half line. We establish the existence of stationary solutions under the Bohm criterion similar to the isentropic case and further obtain the large time asymptotic stability of small-amplitude stationary solutions provided that the initial perturbation is sufficiently small in some weighted Sobolev spaces. Moreover, the convergence rate of the solution toward the stationary solution is obtained. The proof is based on the energy method. A key point is to capture the positivity of the temporal energy dissipation functional and boundary terms with suitable space weight functions either algebraic or exponential depending on whether or not the incoming far-field velocity is critical.