3 papers
math.AP2026
A chemotaxis-consumption model with boundary inflow of a nutrient, steady states
Frederic Heihoff, Piotr Knosalla
In this manuscript we consider the steady state problem for a chemotaxis-consumption model with positive inflow of a nutrient across the boundary. We show that in any bounded smoot…
math.AP2026
Refined temporal asymptotics near blow-up points in the planar Keller-Segel system
Frederic Heihoff, Michael Winkler
For the Keller-Segel system \[ \left\{\, \begin{aligned} u_t &= Îu - \nabla \cdot ( u \nabla v ), \\ v_t &= Îv - v + u \end{aligned} \right. \tag{} \] posed in a planar do…
math.AP2026
Shrinking vs. expanding: the evolution of spatial support in degenerate Keller-Segel systems
Mario Fuest, Frederic Heihoff
We consider radially symmetric solutions of the degenerate Keller-Segel system \begin{align*} \begin{cases} \partial_t u=\nabla\cdot (u^{m-1}\nabla u - u\nabla v),\\ 0=Îv -μ+u,\q…