报告题目： Classification of cubic nonlinear systems and its application to the asymptotic behavior of solutions to dispersive equations. I.

                 Classification of cubic nonlinear systems and its application to the asymptotic behavior of solutions to dispersive equations. II.

报告人：    Satoshi Masaki（日本大阪大学副教授）

报告时间：  2021年12 月13 日 13：00 -14：00

                  2021年12 月14 日 13：00 -14：00

腾讯会议号：861 1699 3165

邀请人：       程 星

报告摘要：In this talk, we consider the asymptotic behavior of solutions to a system of nonlinear dispersive equations with cubic nonlinearity in one space dimension.It is known that the cubic nonlinearity is critical in one dimension in view of the asymptotic behavior and that nonlinearities affect the asymptotic behavior.We restrict ourselves to the case where the system has two unknowns and the nonlinearities are polynomials of the two unknowns with real coefficients.The class of the system is closed under the linear transformation of unknowns. This kind of change defines an equivalence relation between two systems.We classify systems by considering equivalent classes with respect to the equivalence relation. To this end, we introduce a matrix representation of a system.It then turns out that the equivalence relation is clearly formulated and, moreover, the characteristic properties such as conservation laws are well described by the matrix.In the first talk, I will talk about the classification technique. In the second talk, I will discuss its application to the study of the asymptotic behavior of solutions to systems of nonlinear Klein-Gordon equations and of nonlinear Schrodinger equations.

报告人简介：Satoshi Masaki，日本大阪大学工程科学研究院副教授，主要从事非线性色散方程的研究。至今为止，Satoshi Masaki已经完成30多篇学术论文，发表在包括 J. Math. Pures Appl.，Comm. Partial Differential Equations, Anal. PDE, Ann. Inst. H. Poincaré Anal. Non Lineaire, Trans. Amer. Math. Soc.等在内的国际知名期刊。 Satoshi Masaki 主持多项日本学术振兴会(JSPS)的项目，并且于2017年获得日本数学会泛函分析方向的重要奖项福原奖。