Course content

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.

Learning outcome

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.

Learning methods and activities

Lectures, possibly guided self-study.

The course is given every other year, assuming enough students sign up for the course. Next time is Spring 2026. If not enough students register for the course, it will be given as a "ledet selvstudium".

Recommended previous knowledge

The course assumes knowledge corresponding to Matematikk 1-4. The course TMA4305 (Partial Differential Equations) is an advantage.

Course materials

H. Holden, N. H. Risebro: Front Tracking for Hyperbolic Conservation Laws, Springer 2015.