23 citations · 59 across the 12 of their papers we have counts for
12 papers
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…
Refined temporal asymptotics near blow-up points in the planar Keller-Segel system
Frederic Heihoff, Michael Winkler
For the Keller-Segel system \[ \left\{\, \begin{aligned} u_t &= Δu - \nabla \cdot ( u \nabla v ), \\ v_t &= Δv - v + u \end{aligned} \right. \tag{} \] posed in a planar doma…
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=Δv -μ+u,\qua…
Can a chemotaxis-consumption system recover from a measure-type aggregation state in arbitrary dimension?
Frederic Heihoff
We consider the chemotaxis-consumption system \[ \left\{ \begin{aligned} u_t &= Δu - χ\nabla \cdot (u\nabla v) \\ v_t &= Δv - uv \end{aligned} \right. \] in a smooth bounded domain…
Two new functional inequalities and their application to the eventual smoothness of solutions to a chemotaxis-Navier-Stokes system with rotational flux
Frederic Heihoff
We prove two new functional inequalities of the forms\[ \int_G φ(ψ- \overlineψ) \leq \frac{1}{a}\int_G ψ\ln \left(\frac{\;ψ\;}{ \overlineψ}\right) + \frac{a}{4β_0} \left\{ \int_G ψ…
Does strong repulsion lead to smooth solutions in a repulsion-attraction chemotaxis system even when starting with highly irregular initial data?
Frederic Heihoff
It has been well established that, in attraction-repulsion Keller-Segel systems of the form\begin{equation*} \left\{ \begin{aligned} u_t &= Δu - χ\nabla \cdot (u\nabla v) + ξ\nabla…
Global existence and stabilization in a diffusive predator-prey model with population flux by attractive transition
Frederic Heihoff, Tomomi Yokota
The diffusive Lotka-Volterra predator-prey model \begin{eqnarray*} \left\{ \begin{array}{rcll} u_t &=& \nabla\cdot \left[ d_1\nabla u + χv^2 \nabla \Big(\dfrac{u}{v}\Big)\right] +u…
Global solutions to a haptotaxis system with a potentially degenerate diffusion tensor in two and three dimensions
Frederic Heihoff
We consider the potentially degenerate haptotaxis system \begin{equation*} \left\{ \begin{aligned} u_t &= \nabla \cdot (\mathbb{D} \nabla u + u \nabla \cdot \mathbb{D}) - χ\nabla \…
Unboundedness phenomenon in a model of urban crime
Mario Fuest, Frederic Heihoff
We show that spatial patterns ("hotspots") may form in the crime model \begin{equation} \left\{\; \begin{aligned} u_{t} &= \tfrac{1}{\varepsilon}Δu - \tfracχ{\varepsilon} \nabla \c…
On the existence of global smooth solutions to the parabolic-elliptic Keller-Segel system with irregular initial data
Frederic Heihoff
We consider the parabolic-elliptic Keller-Segel system \[ \left\{ \begin{aligned} u_t &= Δu - χ\nabla \cdot (u \nabla v), \\ 0 &= Δv - v + u \end{aligned} \right. \tag{} \]…
Generalized solutions for a system of partial differential equations arising from urban crime modeling with a logistic source term
Frederic Heihoff
We consider the system \[ \left\{ \begin{aligned} u_t &= Δu - χ\nabla \cdot ( \tfrac{u}{v} \nabla v) - uv + ρu - μu^2, \\ v_t &= Δv - v + u v \end{aligned} \right. \tag{} \]…
Global mass-preserving solutions for a two-dimensional chemotaxis system with rotational flux components coupled with a full Navier-Stokes equation
Frederic Heihoff
We study the chemotaxis-Navier-Stokes system \[\left\{\; \begin{aligned} n_t + u\cdot\nabla n &=Δn - \nabla\cdot (nS(x,n,c)\nabla c), &&x\inΩ, t > 0, \\ c_t + u\cdot\nabla c &=Δc -…