Kinetic Approach to Stochastic Conservation Laws

Martina Hofmanova (MPI Leipzig)

June 3 - 26, 2014

Many basic equations in physics can be written in the form of
conservation laws. However, as it is common in the field of PDEs and
SPDEs, classical or strong solutions do not exist in general and, on the
other hand, weak solutions are not unique. The notion of kinetic
formulation and kinetic solution turns out to be a very convenient tool to
overcome these difficulties.
In the first part of this lecture series, we will study deterministic
hyperbolic conservation laws and discuss the main issues one has to face.
Several notions of solution will be discussed, namely, classical
solutions, weak solutions, entropy and kinetic solutions. In the second
part, we will focus on the concept of kinetic solutions, study conservation
laws perturbed by a stochastic noise and present the well-posedness result
developed by Debussche and Vovelle.

The course will not require anything but the standard knowledge of PDEs and
measure theory. 

Everybody is welcome to attend. Students may obtain 3 ECTS Points.