Nonlinear stability

Everyone is familiar with the concepts of Lyapunov stability from the standard course of ordinary differential equations. During the seminar, we will try to figure out what stability is in problems that already contains partial differential equations. Here the concept of nonlinear stability arises. We will study this concept using the example of Vlasov equations. The plan of the first seminar: 1. The general scheme of the method of introducing the energy Casimir functional. 2. Using the energy Casimir functional method in the case of a system of Vlasov-Poisson equation for a single-component plasma in the entire space.