3 citations · 5 across the 5 of their papers we have counts for
5 papers
Avoidance of caldera-type dead cores in a chemotaxis system with degenerate diffusion and compactly supported initial population density
Tobias Black
We consider a degenerate chemotaxis system of the form \begin{align}\label{star}\tag{} \left\lbrace \begin{array}{r@{}l@{\quad}l} &u_t=\nabla\cdot\big(D(u)\nabla u-uS(u)\nab…
Global solutions and large time stabilization in a model for thermoacoustics in a standard linear solid
Tobias Black, Michael Winkler
This manuscript is concerned with the one-dimensional system \[ \begin{array}{l} τu_{ttt} + αu_{tt} = b \big(γ(Θ) u_{xt}\big)_x + \big( γ(Θ) u_x\big)_x, \\[1mm] Θ_t = D Θ_{xx} + bγ…
Very mild diffusion enhancement and singular sensitivity: Existence of bounded weak solutions in a two-dimensional chemotaxis-Navier--Stokes system
Tobias Black
We consider an initial-boundary value problem for the chemotaxis-Navier--Stokes system \begin{align*} \left\{ \begin{array}{c@{\quad}l@{\quad}l@{\,}c} n_{t}+u\cdot\nabla n=\nabla\c…
Refining Hölder regularity theory in degenerate drift-diffusion equations
Tobias Black
We establish the Hölder continuity of bounded nonnegative weak solutions to \begin{align*} \big(Φ^{-1}(w)\big)_t=Δw+\nabla\cdot\big(a(x,t)Φ^{-1}(w)\big)+b\big(x,t,Φ^{-1}(w)\big), \…
Absence of dead-core formations in chemotaxis systems with degenerate diffusion
Tobias Black
In this paper we consider a chemotaxis system with signal consumption and degenerate diffusion of the form \begin{align*} \left\lbrace \begin{array}{r@{}l@{\quad}l} &u_t=\nabla\cdo…