STABILITY FOR SOLUTIONS OF A STATIONARY EULER–POISSON PROBLEM
STABILITY FOR SOLUTIONS OF A STATIONARY EULER–POISSON PROBLEM
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稳态欧拉-泊松问题解的稳定性
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
A. Ambroso
中科院分区：
文献类型：
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作者：
A. Ambroso
研究了等离子体二极管模型的定常Euler-Poisson问题解的稳定性。该模型是在以前的文件，在那里我们证明了存在多个解决方案。由于，从物理上讲，我们希望只有一个解决方案是目前，我们在这里提出两个战略选择的物理固定制度。一方面，我们研究了与驻值问题相关的能量泛函，并根据它们的能级和作为泛函的驻值点对不同的解进行了排序。另一方面，从一个稳定的定态是一个进化后达到的状态的评论，我们数值求解相应的时间依赖的欧拉-泊松问题，并表明，只有一个可能的解决方案确实是稳定的在这个意义上。这两种独立的方法选择相同的解决方案，因此我们将其标记为稳定的。
We study the stability of the solutions of a stationary Euler–Poisson problem modeling a plasma diode. The model was presented in a previous paper, where we proved the existence of multiple solutions. Since, physically speaking, we expect only one solution to be present, we propose here two strategies for selecting the physical stationary regime. On the one hand, we study the energy functional associated with the stationary problem and order the different solutions in terms of their energy level and as stationary points for the functional. On the other hand, starting from the remark that a stable stationary state is the state which is reached after an evolution, we solve numerically the corresponding time-dependent Euler–Poisson problem and show that only one of the possible solutions is indeed stable in this sense. These two independent approaches select the same solution that we label therefore as stable.