论文标题
在一类分散方程的时间复杂近似下的传播特征的稳定性
Stability of propagation features under time-asymptotic approximations for a class of dispersive equations
论文作者
论文摘要
我们考虑通过傅立叶乘数定义的分散方程的频带中的解决方案，这些解决方案被视为波数据包。在本文中，提出了允许时间弥补的现有方法的改进，提出了解决方案公式，从而导致第一个术语继承了真实解的平均位置以及恒定方差误差。特别是，第一个任期在一个时空锥中支持其原点位置明确取决于初始状态，这特别是尤其是改变的时间付费率。该方法考虑了初始状态的空间和频率信息，然后使稳定一些传播特征，并允许对运动解决方案的运动和分散进行更好的描述。首先，通过使溶液公式中的圆锥原点明显出现，其次是通过精确应用具有新误差绑定的固定相位方法的适应版本，最后通过将相对于圆锥原点绑定的误差来最大程度地减少误差。
We consider solutions in frequency bands of dispersive equations on the line defined by Fourier multipliers, these solutions being considered as wave packets. In this paper, a refinement of an existing method permitting to expand time-asymptotically the solution formulas is proposed, leading to a first term inheriting the mean position of the true solution together with a constant variance error. In particular, this first term is supported in a space-time cone whose origin position depends explicitly on the initial state, implying especially a shifted time-decay rate. This method, which takes into account both spatial and frequency information of the initial state, makes then stable some propagation features and permits a better description of the motion and the dispersion of the solutions of interest. The results are achieved firstly by making apparent the cone origin in the solution formula, secondly by applying precisely an adapted version of the stationary phase method with a new error bound, and finally by minimizing the error bound with respect to the cone origin.
