72 citations · 455 across the 28 of their papers we have counts for
4 papers · 2 filters
A cross-diffusion system modelling rivaling gangs: global existence of bounded solutions and FCT stabilization for numerical simulation
Mario Fuest, Shahin Heydari
For the gang territoriality model \begin{align*} \begin{cases} u_t = D_u Δu + χ_u \nabla \cdot (u \nabla w), \\ v_t = D_v Δv + χ_v \nabla \cdot (v \nabla z), \\ w_t = -w + \frac{v}…
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…
On the existence of global solutions for the 3D chemorepulsion system
Tomasz Cieślak, Mario Fuest, Karol Hajduk +1
In this paper, we give sufficient conditions for global-in-time existence of classical solutions for the fully parabolic chemorepulsion system posed on a convex, bounded three-dime…
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),…