9 citations · 13 across the 6 of their papers we have counts for
6 papers
A critical blow-up exponent for flux limitation in a Keller-Segel system
Michael Winkler
The parabolic-elliptic cross-diffusion system \[ \left\{ \begin{array}{l} u_t = Δu - \nabla \cdot \Big(uf(|\nabla v|^2) \nabla v \Big), \\[1mm] 0 = Δv - μ+ u, \qquad \int_Ωv=0, \qq…
Conditional estimates in three-dimensional chemotaxis-Stokes systems and application to a Keller-Segel-fluid model accounting for gradient-dependent flux limitation
Michael Winkler
This manuscript deals with the three-dimensional version of a flux-limited Keller-Segel system coupled to the incompressible Stokes equations through transport and buoyancy. The ma…
Asymptotic stability of spatial homogeneity in a haptotxis model for oncolytic virotherapy
Youshan Tao, Michael Winkler
This work considers a model for oncolytic virotherapy, as given by the reaction-diffusion-taxis system $$ \left\{ \begin{array}{l} u_t = Δu - \nabla \cdot (u\nabla v)-ρuz, \\[1mm]…
Analysis of a one-dimensional forager-exploiter model
Youshan Tao, Michael Winkler
\begin{abstract} \noindent % We consider the one-dimensional parabolic system The system \bas \left\{ \begin{array}{l} u_t= u_{xx} - χ_1 (uw_x)_x, \\[1mm] v_t = v_{xx} - χ_2 (vu_x)…
Boundedness and large time behavior in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity
Michael Winkler
We consider a chemotaxis-fluid system involving nonlinear cell diffusion of porous medium type, signal consumption by cells, and rather general, possibly matrix-valued, chemotactic…
A Continuum of Extinction Rates for the Fast Diffusion Equation
Marek Fila, Juan Luis Vazquez, Michael Winkler
We find a continuum of extinction rates for solutions of the fast diffusion equation in a subrange of exponents . The equation is posed in $\re…