A 3-day summer school on 'Hyperbolic conservation laws' is organised at Hasselt University.
June 25-27, 2018
Many processes are described by physical laws expressing the conservation of mass, momentum, or energy. Commonly, the related mathematical models are systems of partial and ordinary differential equations. One illustrative example is the air flow around planes under standard flight conditions. In mathematical terms, this flow is modelled by the Navier-Stokes or the Euler equations, which form a particular set of mathematical conservation laws.
The focus of the summer school is on hyperbolic conservation laws. The mathematical treatment of conservation laws is a complex and challenging task. In comparison to other types of equations, the hyperbolic conservation laws may have multiple solutions, which may become non-smooth. This makes both the mathematical analysis and the numerical approximation quite cumbersome. Most of the available results are restricted to simplified and hence non-realistic cases, like one-dimensional problems. In the general situations the existence of solutions is still an open research question. Also, in case of multiple solutions, entropy criteria have to be defined to select the physically relevant solution.
Fig. 1: The Mach-number (a normalized velocity) distribution around an idealized airfoil computed as the solution to the Navier-Stokes equations
The goal of this summer school is to give the participants a basic introduction to the analysis and the numerics of hyperbolic conservation laws. The focus will be more on an introduction to the concepts including their applications rather than a complete and rigorous discussion of the theory. All sessions will be hands-on, meaning that sufficient time for exercises and their discussion is planned.
The summer school will be amenable to mathematicians, engineers and scientists and will be presented in a genuine interdisciplinary context. The summer school will be open to participants having a basic knowledge in calculus and linear algebra courses as they are taught to engineers and scientists.