Continuum and kinetic modelling with PDEs
- Unit Coordinator: Anton Arnold
- ECTS Credits: 6
- Semester: 1
- Year: 2
- Campus: Vienna University of Technology
- Language: English
- Aims:
Students will be able to specify and apply a selection of PDE-applications in natural sciences and technology, and to discuss them from a mathematics perspective.
They are able to describe the modelling assumptions or restrictions, as well as their essential analytical and numerical properties.
- Content:
- Fluid dynamical models (Euler, Navier-Stokes, vortex models),
- Traffic flow models,
- Theory of elasticity,
- Hyperbolic conservation laws,
- Image processing models (nonlinear diffusion filter, shock filter),
- Models for pattern formation (reaktion-diffusion equations, Turing instability),
- Evolution of thin films,
- Collective behavior (kinetic equations)
- Pre-requisites:
- Partial differential equations;
- Basic knowledge in physics / mechanics is helpful
- Reading list:
- Lecture notes,
- R. J. LeVeque : Numerical Methods for Conservation Laws, Birkhäuser (1990).
- A.J. Chorin, J.E. Marsden: A mathematical introduction to fluid mechanics, Springer (1990).
- C. Marchioro, M. Pulvirenti: Mathematical theory of incompressible nonviscous fluids, Springer (1994).
- G. Aubert, P. Kornprobst: Mathematical Problems in Image Processing, Springer, New York (2006).
