The concept of entropy is a powerful tool not only in physics and chemistry but also in
mathematics. Entropies allow for the development of new techniques to analyze partial …

The global-in-time existence of bounded weak solutions to a large class of physically
relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure is …

In this paper we extend the famous Keller–Segel model for the chemotactic movement of
motile species to some multi-species chemotaxis equations. The presented multi-species …

In this paper we present an optimal control approach modeling fast exit scenarios in
pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a …

This paper reviews several inverse problems related to biological ion channels and polymer
nanopores. Different problems arise at different scales and thus lead to different inversion …

The brain tumour glioblastoma is characterised by diffuse and infiltrative growth into
surrounding brain tissue. At the macroscopic level, the progression speed of a glioblastoma …

Excluded-volume effects can play an important role in determining transport properties in
diffusion of particles. Here, the diffusion of finite-sized hard-core interacting particles in two …

We consider systems of reaction–diffusion equations as gradient systems with respect to an
entropy functional and a dissipation metric given in terms of a so-called Onsager operator …

A class of parabolic cross-diffusion systems modeling the interaction of an arbitrary number
of population species is analyzed in a bounded domain with no-flux boundary conditions …

Stochastic models of diffusion with excluded-volume effects are used to model many
biological and physical systems at a discrete level. The average properties of the population …