Kinetic schemes of selected initial and boundary value problems

The hyperbolic system that describes heat conduction at low temperatures and the relativistic Euler equations belong to a class of hyperbolic conservation laws that result from an underlying kinetic equation. The focus of this study is the establishment of an kinetic approach in order to solve initial and boundary value problems for the two examples. The ingredients of the kinetic approach are: (i) Representation of macroscopic fields by moment integrals of the kinetic phase density. (ii) Decomposition of the evolution into periods of free flight, which are interrupted by update times. (iii) At the update times the data are refreshed by the Maximum Entropy Principle