9 citations · 56 across the 31 of their papers we have counts for
4 papers · 1 filter
A Keller-Segel type taxis model with ecological interpretation and boundedness due to gradient nonlinearities
Sachiko Ishida, Johannes Lankeit, Giuseppe Viglialoro
We introduce a novel gradient-based damping term into a Keller-Segel type taxis model with motivation from ecology and consider the following system equipped with homogeneous Neuma…
Corners and collapse: Some simple observations concerning critical masses and boundary blow-up in the fully parabolic Keller-Segel system
Mario Fuest, Johannes Lankeit
Our main result shows that the mass is critical for the minimal Keller-Segel system \begin{align}\label{prob:abstract}\tag{} \begin{cases} u_t = Δu - \nabla \cdot (u \n…
Depleting the signal: Analysis of chemotaxis-consumption models -- A survey
Johannes Lankeit, Michael Winkler
We give an overview of analytical results concerned with chemotaxis systems where the signal is absorbed. We recall results on existence and properties of solutions for the prototy…
Critical mass phenomena in higher dimensional quasilinear Keller-Segel systems with indirect signal production
Mario Fuest, Johannes Lankeit, Yuya Tanaka
In this paper, we deal with quasilinear Keller--Segel systems with indirect signal production, $$\begin{cases} u_t = \nabla \cdot ((u+1)^{m-1}\nabla u) - \nabla \cdot (u \nabla v),…