391 citations · 668 across the 36 of their papers we have counts for
4 papers · 1 filter
On a degenerate non-local parabolic problem describing infinite dimensional replicator dynamics
Nikos I. Kavallaris, Johannes Lankeit, Michael Winkler
We establish the existence of locally positive weak solutions to the homogeneous Dirichlet problem for \[ u_t = u Δu + u \int_Ω|\nabla u|^2 \] in bounded domains $Ω\subset\mathbb{R…
Large-data global generalized solutions in a chemotaxis system with tensor-valued sensitivities
Michael Winkler
A chemotaxis system possibly containing rotational components of the cross-diffusive flux is studied under no-flux boundary conditions in a bounded domain , ,…
How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system?
Michael Winkler
A three-dimensional chemotaxis-Navier-Stokes system is considered. It is known that for all suitably regular initial data, a corresponding initial-boundary value problem admits at…
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…