※ Zoom 회의 참가: https://snu-ac-kr.zoom.us/j/8941592643?pwd=L2gxa3k4V2J1V1dFcTNHUnliRkdpdz09
회의 ID: 894 159 2643
Abstract: In this talk, I will introduce a concept of (finite and infinite-dimensional) dynamical systems incorporated with Hamiltonian structure and discuss several kinds of stability concepts for stationary states to them, including linearized or nonlinear stability. We will see that in any case for the Hamiltonian dynamical system, the linearized stability doesn't imply nonlinear stability due to the existence of a pure imaginary eigenvalue for the linearized operators. The main purpose of this talk is to explain, with rather simple finite-dimensional examples, the variational approach is one of the good methodologies for bypassing this subtlety to deduce the nonlinear stability for Hamiltonian dynamical systems. If time permits, I will also show how to naturally extend these ideas to infinite-dimensional nonlinear PDEs such as nonlinear Schrodinger equations or Euler-Poisson equations.