Speaker: Jun Yan (Fudan University)
Abstract: Recent advances in the theory of Lyapunov stability for viscosity solutions of contact-type Hamilton-Jacobi equations are introduced. Sufficient conditions for asymptotic stability and instability are provided, and criteria for verifying these conditions are established using the auxiliary function method for several typical classes of equations.
Time： Sept. 18 2025 Thursday，14:00-16:00
Location: R1310，SIMIS
Introduction to the speaker: Jun Yan is a professor and doctoral advisor at the School of Mathematical Sciences, Fudan University. He has long been engaged in the study of Hamiltonian dynamical systems and has achieved a series of breakthroughs in areas such as the Aubry-Mather theory of contact dynamical systems and the viscosity solution theory of Hamilton-Jacobi equations. In 2013, he was awarded the National Science Fund for Distinguished Young Scholars. In 2014, he was appointed as a Chang Jiang Scholar Distinguished Professor by the Ministry of Education, and in 2016, he was selected as a leading talent of the National Ten Thousand Talent Program by the Organization Department of the CPC Central Committee. In collaboration with peers, he introduced the implicit variational principle into general Hamilton-Jacobi equations and developed it into an independent weak KAM theory, achieving a series of significant results, including the existence of periodic solutions for Hamilton-Jacobi equations and the stability of viscosity solutions.
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