We propose a second order finite volume scheme for nonlinear degenerate parabolic
equations which admit an entropy functional. For some of these models (porous media …

The aim of this paper is to discuss the effects of linear and nonlinear diffusion in the large
time asymptotic behavior of the Keller–Segel model of chemotaxis with volume filling effect …

We propose a mixed finite element method for a class of nonlinear diffusion equations,
which is based on their interpretation as gradient flows in optimal transportation metrics. We …

We analyze stability of conservative solutions of the Cauchy problem on the line for the
(integrated) Hunter–Saxton (HS) equation. Generically, the solutions of the HS equation …

The aim of this paper is to analyze contractivity properties of Wasserstein-type metrics for
one-dimensional scalar conservation laws with nonnegative, L∞ and compactly supported …

A multiscale meshfree particle method for macroscopic mean field approximations of
generalized interacting particle models is developed and investigated. The method is …

In this paper, we study the asymptotic behavior of the solutions of the system of non-linear
partial differential equations studied in [ESG05] for the evolution of a family of …

A multiscale meshfree particle method for macroscopic mean field approximations of
interacting particle models is developed. The method is working for a large range of …

Being able to measure the spatial motion of arbitrary objects with high accuracy and low
latency is vital for numerous higher level tasks in many fields of application. These include …

A nonlinear degenerate Fokker-Planck equation in the whole space is analyzed. The
existence of solutions to the corresponding implicit Euler scheme is proved, and it is shown …