论文标题
复杂指数的生物表定功能，并通过瞬间方法应用Kawahara方程的可控性
Biorthogonal functions for complex exponentials and an application to the controllability of the Kawahara equation via a moment approach
论文作者
论文摘要
该论文介绍了在周期域上提出的卡瓦哈拉方程的可控性能。我们表明，该方程仅根据时间而定，并通过空间中给定的形状函数在系统上作用。首先，通过解决方案的傅立叶扩展以及对复杂指数函数家族的生物三相序列的分析，为线性化系统建立了确切的可控性能。最后，通过将线性化系统的分析，固定点参数和Kawahara方程在周期域上的某些波尔加因平滑属性结合来得出完整系统的局部可控性。
The paper deals with the controllability properties of the Kawahara equation posed on a periodic domain. We show that the equation is exactly controllable by means of a control depending only on time and acting on the system through a given shape function in space. Firstly, the exact controllability property is established for the linearized system through a Fourier expansion of solutions and the analysis of a biorthogonal sequence to a family of complex exponential functions. Finally, the local controllability of the full system is derived by combining the analysis of the linearized system, a fixed point argument and some Bourgain smoothing properties of the Kawahara equation on a periodic domain.
