Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

DMV Tagung 2011 - Köln, 19. - 22. September
Friedrich Lippoth
Leibniz Universität Hannover
Classical solutions for a one phase osmosis model
For a moving boundary problem modelling the motion of a semipermeable membrane by osmotic
pressure and surface tension we prove the existence and uniqueness of classical solutions on small time
intervals. Moreover, we construct solutions existing on arbitrary long time intervals, provided the initial
geometry is close to an equilibrium. In both cases, our method relies on maximal regularity results for
parabolic systems with inhomogeneous boundary data.
Thomas Marquardt
MPI Golm
A Neumann Problem for Inverse Mean Curvature Flow
In this talk we consider hypersurfaces with boundary in Euclidean space which evolve in the direction of
the unit normal with speed equal to the reciprocal of the mean curvature. We choose Neumann boundary
conditions, i.e. the hypersurface moves along but stays perpendicular to a fixed supporting hypersurface.
After short time existence for that nonlinear parabolic Neumann problem is established we will concentrate
on the case where the supporting hypersurface is a convex cone. In this case we obtain long time
existence and convergence to a piece of a round sphere.
If time permits we will present an approach to define weak solutions using a level set formalism which
leads to a mixed Dirichlet-Neumann problem.
Anca Matioc
Leibniz Universität Hannover
Analysis of a two-phase model describing the growth of solid tumors
We consider a two-phase model describing the growth of avascular solid tumors which takes into account
the effects of cell-to-cell adhesion and taxis due to nutrient.
We prove that the mathematical model is well-posed and determine all radially symmetric steady-state
solutions of the problem. Furthermore, we also study the stability properties of the radially symmetric
equilibria in dependence of the biophysical parameters involved in the problem.
This is a joint work with J. Escher.
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