2018年信息与数学学院学术报告(二十一)

讲座题目: Asymptotic stability of the phase-homogeneous solution to the Kuramoto-Sakaguchi equation with inertia

主办单位:信息与数学学院

报告专家:肖清华(中国科学院武汉物理与数学研究所副研究员)

报告时间:20181016日(周二)下午16:00-17:30

报告地点:8406

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摘要:We present the global-in-time existence of strong solutions and its large-time behavior for the Kuramoto-Sakaguchi equation with inertia. The equation describes the evolution of the probability density function for a large ensemble of Kuramoto oscillators under the effects of inertia and stochastic noises. We consider a perturbative framework around the equilibrium, which is a Maxwellian type, and use the classical energy method together with our careful analysis on the macro-micro decomposition. We establish the global-in-time existence and uniqueness of strong solutions when the initial data are sufficiently regular, not necessarily close to the equilibrium, and the noise strength is also large enough. For the large-time behavior, we show the exponential decay of solutions towards the equilibrium under the same assumptions as those for the global regularity of solutions.

专家简介:肖清华,2012年博士毕业于武汉大学数学与统计学院,2012年至2014年在韩国首尔国立大学做博士后研究,现为中国科学院武汉物理与数学研究所副研究员,2017入选中国科学院青年创新促进会会员,主要从事Boltzmann型方程、与Kuramoto方程和Cucker-Smale方程相关动理学方程、守恒律方程方面的研究。目前在Journal of Functional AnalysisSIAM Journal on Mathematical  AnalysisMathematical Models and Methods in Applied SciencesJournal of Differential Equations 等期刊发表论文20余篇。