After successful completion of the course, students are able to understand and explain applications, derivations, reseults of the mathematical analysis, and some numerical schemes of kinetic equations.
1. Applications, derivation of kinetic equations from particle systems
2. Mathematical analysis of Cauchy and boundary value problems
3. Quantum-kinetic equations, semi-classical limit
4. Hydrodynamic limits
5. Numerical methods
H. Babovsky, Die Boltzmann-Gleichung, Teubner, 1998
F. Bouchut, F. Golse, M. Pulvirenti, Kinetic equations and asymptotic theories, Elsevier, 2000
C. Cercignani, R. Illner, M. Pulvirenti, The Mathematical Theory Of Dilute Gases, Springer, 1994
C. Cercignani, The Boltzmann equation and its appplications, Springer, 1998
C. Cercignani, Rarefied Gas Dynamics - From Basic Concepts to Actual Calculations, Cambridge University Press, 2000
C. Villani, A review of mathematical topics in collisional kinetic theory. Handbook of mathematical fluid dynamics, Vol. I, 71-305, North-Holland, Amsterdam, 2002 (S. Friedlander & D. Serre, Eds)
Link: https://www.cedricvillani.org/sites/dev/files/old_images/2012/07/B01.Handbook.pdf
R.T. Glassey, The Cauchy Problem in Kinetic Theory, SIAM, 1996
P.A. Markowich, C.A. Ringhofer, C. Schmeiser, Semiconductor Equations, Springer, 1990
C. Mouhot, course "Mathematical Topics in Kinetic Theory", Link: https://cmouhot.wordpress.com/1900/10/25/mathematical-topics-in-kinetic-theory-part-iii-course/
