63 citations · 340 across the 15 of their papers we have counts for
17 papers
Subcritical-mass global solvability in a doubly degenerate Keller-Segel system with signal production
Tobias Black, Genglin Li
We consider the initial-boundary value problem for a variant of the Keller-Segel chemotaxis system with doubly degenerate diffusion, i.e. we study \[ \left\{ \begin{array}{ll} u_t…
Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source
Tobias Black, Mario Fuest, Johannes Lankeit +1
We discuss the influence of possible spatial inhomogeneities in the coefficients of logistic source terms in parabolic-elliptic chemotaxis-growth systems of the form \begin{align*}…
Prescribed signal concentration on the boundary: Weak solvability in a chemotaxis-Stokes system with proliferation
Tobias Black, Chunyan Wu
We study a chemotaxis-Stokes system with signal consumption and logistic source terms of the form \noindent \begin{align*} \left\{ \begin{array}{r@{\ }l@{\quad}l@{\quad}l@{\,}c} n_…
Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic-elliptic Keller-Segel systems
Tobias Black, Mario Fuest, Johannes Lankeit
We study the finite-time blow-up in two variants of the parabolic-elliptic Keller-Segel system with nonlinear diffusion and logistic source. In -dimensional balls, we consider \…
Global generalized solutions to a forager-exploiter model with superlinear degradation and their eventual regularity properties
Tobias Black
In this article we consider a cascaded taxis model for two proliferating and degrading species which thrive on the same nutrient but orient their movement according to different sc…
The Stokes limit in a three-dimensional chemotaxis-Navier-Stokes system
Tobias Black
We consider initial-boundary value problems for the -dependent family of chemotaxis-(Navier--)Stokes systems \begin{align*} \left\{ \begin{array}{r@{\,}c@{\,}c@{\ }l@{\quad}l@{\…
Stabilization in the Keller--Segel system with signal-dependent sensitivity
Tobias Black, Johannes Lankeit, Masaaki Mizukami
This paper deals with the Keller--Segel system with signal-dependent sensitivity \begin{align*} &u_t = Δu - χ\nabla \cdot (uS(v)\nabla v), &v_t = Δv - v + u, \end{align*} where $χ>…
Global solvability of chemotaxis-fluid systems with nonlinear diffusion and matrix-valued sensitivities in three dimensions
Tobias Black
In this work we extend a recent result to chemotaxis fluid systems which include matrix-valued sensitivity functions in addit…
A Keller-Segel-fluid system with singular sensitivity: Generalized solutions
Tobias Black, Johannes Lankeit, Masaaki Mizukami
In bounded smooth domains , , we consider the Keller-Segel-Stokes system \begin{align*} n_t + u\cdot \nabla n &= Δn - χ\nabla \cdot(\frac{n}{c}\n…
Global very weak solutions to a chemotaxis-fluid system with nonlinear diffusion
Tobias Black
We consider the chemotaxis-fluid system \begin{align}\label{star}\tag{} \left\{ \begin{array}{r@{\,}c@{\,}c@{\ }l@{\quad}l@{\quad}l@{\,}c} n_{t}&+&u\cdot\!\nabla n&=Δ…
Singular sensitivity in a Keller-Segel-fluid system
Tobias Black, Johannes Lankeit, Masaaki Mizukami
In bounded smooth domains , , considering the chemotaxis--fluid system \[ \begin{cases} \begin{split} & n_t + u\cdot \nabla n &= Δn - χ\nabla \cd…
Global generalized solutions to a parabolic-elliptic Keller-Segel system with singular sensitivity
Tobias Black
We investigate the parabolic-elliptic Keller-Segel model \begin{align*}\left\{\begin{array}{r@{\,}l@{\quad}l@{\quad}l@{\,}c} u_{t}&=Δu-\,χ\nabla\!\cdot(\frac{u}{v}\nabla v),\ &x\in…
Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes system
Tobias Black
We study the chemotaxis-fluid system \begin{align*} \left\{ \begin{array}{r@{\,}c@{\,}c@{\ }l@{\quad}l@{\quad}l@{\,}c} n_{t}&+&u\cdot\!\nabla n&=Δn-\nabla\!\cdot(\frac{n}{c}\nabla…
On the weakly competitive case in a two-species chemotaxis model
Tobias Black, Johannes Lankeit, Masaaki Mizukami
In this article we investigate a parabolic-parabolic-elliptic two-species chemotaxis system with weak competition and show global asymptotic stability of the coexistence steady sta…
Sublinear signal production in a two-dimensional Keller-Segel-Stokes system
Tobias Black
We study the chemotaxis-fluid system \begin{align*} \left\{\begin{array}{r@{\,}l@{\quad}l@{\,}c} n_{t}&=Δn-\nabla\!\cdot(n\nabla c)-u\cdot\!\nabla n,\ &x\inΩ,& t>0,\\ c_{t}&=Δc-c+f…
Blow-up of weak solutions to a chemotaxis system under influence of an external chemoattractant
Tobias Black
We study nonnnegative radially symmetric solutions of the parabolic-elliptic Keller-Segel whole space system \begin{align*} \left\{\begin{array}{c@{\,}l@{\quad}l@{\,}c} u_{t}&=Δu-\…
Boundedness in a Keller-Segel system with external signal production
Tobias Black
We study the Neumann initial-boundary problem for the chemotaxis system \begin{align*} \left\{\begin{array}{c@{\,}l@{\quad}l@{\,}c} u_{t}&=Δu-\nabla\!\cdot(u\nabla v),\ &x\inΩ,& t>…