主讲人简介：穆春来教授、博导，重庆大学数学与统计学院副院长（主持工作），长期从事抛物偏微分方程方面的研究工作。

报告摘要：This talk will address that the Cauchy problem of Rosenau equation is global well-posed for initial data in H^s(R)(s> 0), and ill-posed for initial data in H^s(R)(s < 0) in the sense that the flow mapping is not continuous at the origin fromH^s(R) to D'(R) at any fixed t > 0 small enough. Moreover, it is showedthat the solution to the Cauchy problem of Rosenau equation has uniquecontinuation property under two sufficient conditions on initial data. On the other hand, It is also proved that the initial boundary value problem has a unique global distributional solution, and thesolution mapping is Lipschitz continuous in a neighborhood of initial data.