动力学Kuramoto方程的Wasserstein度规的收缩性
Contractivity of the Wasserstein metric for the kinetic Kuramoto equation
摘要：
我们提出了同步和收缩估计的动力学仓本模型从仓本相模型的平均场极限。对于全同的Kuramoto振子，我们给出了一类可容许的初始数据，使得所有的测度值解都收敛于集中在初始平均相位上的旅行Dirac测度.如果两个初始Radon测度具有相同的固有频率密度函数和耦合强度，我们证明了相应测度值解之间的Wasserstein p-距离随时间呈指数递减.这个收缩原理比以前的仓本相模型的L1-收缩性质更一般。
英文摘要：
We present synchronization and contractivity estimates for the kinetic Kuramoto model obtained from the Kuramoto phase model in the mean-field limit. For identical Kuramoto oscillators, we present an admissible class of initial data leading to time-asymptotic complete synchronization, that is, all measure valued solutions converge to the traveling Dirac measure concentrated on the initial averaged phase. If two initial Radon measures have the same natural frequency density function and strength of coupling, we show that the Wasserstein p-distance between corresponding measure valued solutions is exponentially decreasing in time. This contraction principle is more general than previous L1-contraction properties of the Kuramoto phase model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
