The weak KAM theorem tells us that the dynamical behavior of the semiflow generated by the Hamilton-Jacobi equation, which originates from classical mechanics, is simple. However, the dynamical behavior of the semiflow generated by the contact Hamilton-Jacobi equation, which has profound backgrounds in fields such as thermodynamics, is completely different. This talk will cover topics related to the (in)stability, the existence and multiplicity of periodic and quasi-periodic solutions, as well as chaotic phenomena, concerning the contact Hamilton-Jacobi equation.

报告人简介

王楷植，上海交通大学特聘教授。主要从事Hamilton动力系统的研究，在弱KAM理论及其在Hamilton-Jacobi方程和平均场博弈系统中的应用等方面做出了系列工作，相关成果发表于《Calc. Var. Partial Differential Equations》，《Comm. Math. Phys.》，《J. Funct. Anal.》，《J. Math. Pures Appl.》，《Math. Ann.》，《SIAM J. Math. Anal.》，《Sci. China Math.》等学术期刊。2022年获上海高校特聘教授（东方学者）计划资助，2025年获国家自然科学基金青年科学基金项目（A类）资助。现任上海市非线性科学研究会理事，《Studies in Applied Mathematics》青年编委。