论文标题
广义对称的正规化长波系统的适合性和可控性
The Well-posedness and Controllability of the Generalized Symmetric Regularized Long Wave System
论文作者
论文摘要
对称的正规化长波系统（SRLW）是弱非线性离子声和空间充电波的模型，该模型由C. Seyler和D. fenstermacher引入。在本文中，我们研究了不同结构（周期性和有界域）中广义对称性长波系统（G-SRLW）的良好性和可控性能。首先，在分布式移动控制的效果下获得了在一维圆环上构成的线性和非线性G-SRLW系统的良好性和确切的可控性结果。其次，我们以某些Dirichlet-Neumann条件为有界间隔的G-SRLW系统，我们表明该系统在频谱上不可控制（没有与状态方程相关的特征函数的有限线性组合，除了零以外，可以将其转向为零）。尽管系统不能在频谱上可控，但可以证明它是近似可控的。
The symmetric regularized long wave system (SRLW) is a model for the weakly nonlinear ion acoustic and space-charge waves, which was introduced by C. Seyler and D. Fenstermacher. In this paper, we investigated the wellposedness and controllability properties of the generalized symmetric regularized long wave system (g-SRLW) in different structures (periodic and bounded domains). Firstly, the wellposedness and the exact controllability results for both linear and nonlinear g-SRLW system posed on the one-dimensional torus are obtained under the effect of a distributed moving control. Second, we consider the g-SRLW system in a bounded interval with some Dirichlet-Neumann conditions and we show that the system is not spectrally controllable (No finite linear combination of eigenfunctions associated with the state equations, other than zero, can be steered to zero). Although the system is not spectrally controllable, it can be shown that it is approximately controllable.
