16h00 [Martina HOFMANOVA] (Prague).

       Kinetic approach to degenerate parabolic SPDEs (Part III)

ABSTRACT. Many basic equations in physics can be written in the form of conservation laws or degenerate parabolic partial differential equations. 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 solution for degenerate parabolic-hyperbolic PDEs perturbed by a stochastic noise and study the proof of well-posedness.