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Kinetic Theory & Approximation (John von Neumann Lecture)

Module MA5053
Credits 2 SWS
Lecturer Prof. Francis Filbet Pfeil
Examination Oral


Course content

I. Transport equations II. The Vlasov-Poisson system [1]
III. Dispersion lemma
IV. Approximation of transport equations

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.

Course literature

[1] F. Bouchut, F. Golse, M. Pulvirenti, Kinetic equations and asymptotic theory, Series in Appl. Math., Gauthiers-Villars, 2000

[2] F. Bouchut, Nonlinear stability of finite volume methods for hyperbolic conservation laws, and well-balanced schemes for sources, Frontiers in Mathematics series, Birkhäuser, 2004

[3] Terence Tao, Nonlinear dispersive equations: local and global analysis, , CBMS regional conference series in mathematics