Tid: 2 april 2012 kl 15.15-16.00.

Föredragshållare: Jan-Frederik Pietschmann, CIAM/matematisk statistik, KTH

Titel: Human crowd motion and inverse problems

Abstract A good understanding of the motion of (human) crowds becomes increasingly important due to the growing fraction of humanity living in urban regions. Appropriate mathematical models can help to optimize buildings and other facilities in order to avoid congestion and allow for faster operation. However, there are several difficulties in formulating such a model, especially for high densities. In this talk we therefore formulate a class of inverse problems of particular relevance in crowded motion, namely the simultaneous identification of entropies and mobilities in nonlinear drift-diffusion equations. We study a model case of this class, which is the identification from flux-based measurements in a stationary setup. This leads to an inverse problem for a non-linear transport-diffusion model, where boundary values and possibly an external potential can be varied. We verify the simultaneous identifiability of the non-linearities and present several numerical tests yielding further insight on the way variations in boundary values and external potential affect the quality of reconstructions.

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