Course Unit


Continuum and kinetic modelling with PDEs

Unit Coordinator: Anton Arnold, Markus Melenk
Programme: Erasmus Mundus
ECTS Credits: 6
Semester: 1
Year: 2
Campus: Vienna University of Technology
Language: English

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.

  • 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)
  • 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).


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