论文标题
完整的Euler-Poisson系统中的半空间问题
A half-space problem on the full Euler-Poisson system
论文作者
论文摘要
本文涉及一半以上离子的完整Euler-Poisson系统上的初始价值问题。我们在BOHM标准下建立了固定溶液的存在，只要在某些加权的Sobolev空间中，小振幅固定溶液的近时间渐近稳定性就足够小。此外，获得溶液向固定溶液的收敛速率。证明基于能量法。一个关键点是根据临时能量耗散功能和边界术语的阳性术语，具有适当的空间重量功能，以代数或指数呈指数，具体取决于传入的远场速度是否至关重要。
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.
