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The research field of Peter Markowich is the mathematical and numerical
analysis
of partial differential equations (PDEs) and their application in physics,
biology and engineering.
In particular he is interested in
*classical and quantum mechanical kinetic theory
*analytical and numerical problems occuring in highly oscillatory
PDEs (like semiclassical asymptotics)
*Wigner transforms
*nonlinear PDEs describing dispersive and, resp., diffusive phenomena
*singular perturbations and long-time asymptotics
*generalized Sobolev inequalities
*inverse problems in solid state physics
*image processing using PDEs.
The main application areas of current interest are
*Bose-Einstein condensation
*charge transport in plasmas and semiconductors
*chemotaxis.
*socioeconomics
Please visit also
http://www.damtp.cam.ac.uk/people/p.markowich/ .
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