# Kinetic Theory & Approximation (John von Neumann Lecture)

Module | MA5053 |
---|---|

Credits | 2 SWS |

Lecturer | Prof. Francis Filbet ^{} |

Examination | Oral |

## Dates

- 11.11.2015 14:00-17:00 03.04.011
- 18.11.2015 14:00-17:00 03.04.011
- 25.11.2015 14:00-17:00 03.04.011
- 02.12.2015 14:00-17:00 03.04.011
- 09.12.2015 14:00-17:00 03.04.011
- 16.12.2015 14:00-17:00 03.04.011

## Course content

I. Transport equations- Theory of characteristics for linear equation
- Existence and uniqueness of weak and classical solutions

- existence of weak solutions : solutions à la Di Perna-Lions
- Averaging lemma : regularizing effects on transport equations
- Application to the Vlasov-Maxwell system

- Strichartz estimates on transport equations [3]

- Finite volume method [2]
- Stability and convergence results

**Intended learning outcome**: After successful completion of the module, students will be able to master simple problems of kinetic theory, deal with useful basic tool in partial differential equations, better understand classical transport equations and Vlasov-Poisson systems.

**Prerequisites**: Students are supposed to have a Bachelor degree in Mathematics, Physics or Computer Science. Some basic notions of Partial Differential Equations are needed, and some knowledge of functional analysis (such as weak convergence) and measure theory may be helpful, even though not strictly necessary.