Iulia Cristian: From one-dimensional coagulation models to multi-dimensional ones

Speaker
Iulia Cristian, University of Bonn

Abstract
Multi-dimensional coagulation equations have been used in recent years in order to include information about the system of particles which cannot be otherwise incorporated. Depending on the model, we can describe in addition to the evolution of the size-distribution of particles, the evolution of the shape, chemical composition or position in space of clusters. We start by discussing such examples of multicomponent coagulation equations.
We then focus on an inhomogeneous two-dimensional model that contains a transport term in the spatial variable modeling the sedimentation of clusters. We prove local existence of mass conserving solutions for a class of coagulation kernels for which in the space homogeneous case instantaneous gelation (i.e., instantaneous loss of mass) occurs. This includes the case of sum-type kernels of homogeneity greater than one for which solutions do not exist in the space homogeneous case.
The last part of the talk is based on a joint work with B. Niethammer (U. Bonn) and J. J. L. Velázquez (U. Bonn).