27May 2016
11:00 - 12:00

Seminar in Numerical Analysis: Ana Djurdjevac (FU Berlin)

Parabolic equations with random coefficients on moving hypersurfaces

Sometimes the partial differential equations with random coefficients can be better formulated on moving domains, especially in biological applications. We will introduce and analyse the advection-diffusion equations with random coefficients on moving hypersurfaces. Under suitable regularity assumptions, using Banach-Necas-Babuska theorem, we will prove existence and uniqueness of the weak solution and also we will give some regularity results about the solution. For discretization in space, we will apply the evolving surface finite element method. In order to deal with uncertainty, we will use Monte Carlo method. Furthermore, we plan to discuss the case when the velocity of the hypersuraface is random.

This is a joint work with Charles M. Elliott (University of Warwick, UK), Ralf Kornhuber (Free University Berlin, Germany) and Thomas Ranner (University of Leeds, UK).


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