This class is an introduction to the mathematical study of models from the Kinetic Theory of Plasmas. The intent is to learn essential tools and techniques for the study of Partial Differential Equations while applying them to some of the most important equations of Kinetic Theory: Vlasov equations.
Content of the course:
Weak solutions to conservative transport equations
Kinetic theory of Plasmas
Mean field limit
From particles model to Vlasov-Poisson
Dobrushin’s stability theorem
The Cauchy problem for Vlasov-Poisson
Required: Notions in functional analysis, differential equations and Lebesgue integration
Optional: Distribution theory, Sobolev spaces, notions in elliptic PDEs
Rules of the Seminar Class
To obtain the credits for the seminar each student must:
Give a 40min presentation on an assigned topic
Attend at least 9 of the 13 lectures
Submit the solutions of any exercise present in the part of the lecture notes associated with the assigned topic
Students are encouraged to work in pairs in order for the two presentations given during a Lecture to be coordinated and complementary. We strongly advise the students to do a mock presentation with their partner to ensure that the time limit of 40 minutes is respected and that the two presentations are clear and well-structured.
The topics and associated parts of the Lecture notes will be assigned to pairs of students two weeks before the presentation is due.