applied math seminar
Title: Bifurcations in the Vlasov equation
The Vlasov equation models the dynamics of a large number of interacting particles, when the force acting on them is dominated by the mean-field (i.e. one particle feels the overall effect of the others). It is a fundamental equation of plasma physics and galactic dynamics, but also describes a number of other physical systems, such as wave-particles interactions, free electron lasers, certain regimes of nonlinear optics, and wave propagation in bubbly fluids. Understanding the qualitative behavior of this nonlinear partial differential equation has proved to be a formidable challenge, from the first linear computations of Landau to the most recent mathematical breakthroughs.
In this talk, I will present some of the basics motivations, properties and questions associated with the study of this equation, like how to derive it from the Newton equations and how to use it in real physics problems.
Then I will present my work on the nonlinear dynamics (bifurcations study) of the Vlasov equation. The theoretical results will be illustrated by some numerical simulations.
Contact Name: Pavel Lushnikov