Non-Linear Hyperbolic Conservation Laws

Fundamental mathematical and numerical properties for conservation laws include: Existence of solutions, shock solutions, entropy conditions, Rankine-Hugoniot condition. Numerical techniques include front tracking, finite difference methods, Riemann solvers, and Glimm's method. Applications to gas dynamics and petroleum reservoirs will be discussed.

1. Knowledge. The course covers fundamental mathematical and numerical properties for conservation laws, in particular: Existence of solutions, shock solutions, entropy conditions, Rankine-Hugoniot condition. Numerical techniques include front tracking, finite difference methods, Riemann solvers, and Glimm's method 2. Skills. The students should be able to handle problems and conduct researches on nonlinear partial differential equations and their applications, in particular applications to gas dynamics and petroleum reservoirs as well as to other applied disciplines 3. Competence. The students should be able to participate in scientific discussions and conduct researches on high international level as well as collaborate in joint interdisciplinary researches.

Lectures, possibly guided self-study.

The course will be taught as needed. If there are few PhD students, the course is only given as a guided self-study.