Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

Jürgen Saal
Universität Konstanz
Analysis of a General Model in Electrokinetics
DMV Tagung 2011 - Köln, 19. - 22. September
We present a thorough analysis of the Navier-Stokes-Nernst-Planck-Poisson equations. This system
describes the dynamics of charged particles dispersed in an incompressible fluid. In contrast to existing
literatur and in view of its physical relevance, we also allow for different diffusion coefficients of the
charged species. Our aim is to present results on local and global well-posedness as well as (in-) stability
of equilibria. The results are obtained jointly with Andre Fischer.
Daniela Treutler
Leibniz Universität Hannover
On the behaviour of solutions to a parabolic evolution equation on two scales
We consider solutions to a distributed microstructure model in the sense of Showalter and Walkington
that describes solute transport in fissured porous media. It reflects the geometry of the porous blocks
inside the material. The coupling of the equations is represented by a source term on the macroscopic
scale and a matching boundary condition on the microscopic one. For Dirichlet boundary conditions on
the large domain we show that the concentration decays exponentially fast in time. On the other hand a
no-flux condition on the macroscopic domain assures conservation of the amount of solute in the whole
system.
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