391 citations · 668 across the 36 of their papers we have counts for
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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 $$ \left\{ \begin{array}{l} u_t = Δu - \nabla \cdot (u\nabla v)-ρuz, \\[1mm]…
Relaxation by nonlinear diffusion enhancement in a two-dimensional cross-diffusion model for urban crime propagation
Nancy Rodriguez, Michael Winkler
We consider a class of macroscopic models for the spatio-temporal evolution of urban crime, as originally going back to Short et al. (Math. Mod. Meth. Appl. Sci. 18, 2008). The foc…
Existence theory and qualitative analysis for a fully cross-diffusive predator-prey system
Youshan Tao, Michael Winkler
This manuscript considers a Neumann initial-boundary value problem for the predator-prey system $$ \left\{ \begin{array}{l} u_t = D_1 u_{xx} - χ_1 (uv_x)_x + u(λ_1-u+a_1 v), \\[1mm…