有界区间上动力学等离子体鞘层的线性与非线性稳定性
Linear and Non linear stability for the kinetic plasma sheath on a bounded interval
AI总结：
本文研究了有界区间上Vlasov-Poisson型系统中动力学等离子体鞘层稳态的线性与非线性稳定性，证明了在注入速率小于吸收速率时涨落指数衰减，并在小平衡态和小局部扰动条件下得到非线性稳定性结果。
摘要：
等离子体鞘层是等离子体与吸收壁接触时形成的非均匀稳态。我们证明了在Vlasov-Poisson型系统中，有界区间上动力学鞘层稳态的线性与非线性稳定性。值得注意的是，在线性情形下，只要平衡态下粒子的注入速率小于壁面处的吸收速率，我们就得到了涨落的指数衰减。在非线性情形下，对于足够小的平衡态以及平衡态的小局部扰动，我们证明了类似的结果。
英文摘要：
Plasma sheaths are inhomogeneous stationary states that form when a plasma is in contact with an absorbing wall. We prove linear and non linear stability of a kinetic sheath stationary state for a Vlasov-Poisson type system in a bounded interval. Notably, in the linear setting, we obtain exponential decay of the fluctuation provided the rate of injection of particles at equilibrium is smaller than the rate of absorption at the wall. In the non linear setting, we prove a similar result for small enough equilibrium and small localized perturbation of the equilibrium.
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