Highly Oscillatory PDEs
Peter Markowich
Universität Wien, Austria

Abstract. Partial differential equations with highly oscillatory solutions 
occur in many areas of science like quantum mechanics and acoustics, with 
important spin-offs to semiconductors,
nanotechnology and low-temperature physics.
These equations pose a great challenge to mathematical and numerical 
analysis. Recently a new mathematical technique has been developed to 
treat highly oscillatory PDEs, namely
Wigner transforms. They allow deep new insights into high-frequency 
asymptotics. The state-of-the-art is reported in the lecture, with 
emphasis on applications like quantum
semiconductor devices and Bose-Einstein condensation.