四分之一平面上BBM方程的一种新的解表示及其最终周期性
A new solution representation for the BBM equation in a quarter plane and the eventual periodicity
摘要：
研究了Benjamin-Bona-Mahony（BBM）方程的初边值问题边值问题.我们的目标是了解其解对应于周期边界条件或周期强迫的周期行为（称为最终周期性）。为了这个目的，我们推导出一个新的公式表示这个初始和边值问题的解决方案，通过反转的运营商$\partial_t +α\partial_x -γ\partial_{xxt}$中定义的时空四分之一平面。将新的表示式与定相稳定相位法相结合，建立了具有周期边界数据和强迫项的线性化BBM方程的最终周期性。
英文摘要：
The initial- and boundary-value problem for the Benjamin-Bona-Mahony (BBM) equation is studied in this paper. The goal is to understand the periodic behavior (termed as eventual periodicity) of its solutions corresponding to periodic boundary condition or periodic forcing. To this aim, we derive a new formula representing solutions of this initial- and boundary-value problem by inverting the operator $\partial_t +α\partial_x -γ\partial_{xxt}$ defined in the space-time quarter plane. The eventual periodicity of the linearized BBM equation with periodic boundary data and forcing term is established by combining this new representation formula and the method of stationary phase.
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