391 citations · 668 across the 36 of their papers we have counts for
5 papers · 1 filter
Critical mass for infinite-time aggregation in a chemotaxis model with indirect signal production
Youshan Tao, Michael Winkler
We study the Neumann initial-boundary problem for the chemotaxis system $$ \left\{\begin{array}{ll} u_t= Δu - \nabla \cdot (u\nabla v), & x\in Ω, \, t>0, 0=Δv - μ(t)+w, & x\in Ω, \…
A degenerate chemotaxis system with flux limitation: Finite-time blow-up
Nicola Bellomo, Michael Winkler
This paper is concerned with radially symmetric solutions of the parabolic-elliptic version of the Keller-Segel system with flux limitation, as given by \begin{equation} \left\{ \b…
A degenerate chemotaxis system with flux limitation: Maximally extended solutions and absence of gradient blow-up
Nicola Bellomo, Michael Winkler
This paper aims at providing a first step toward a qualitative theory for a new class of chemotaxis models derived from the celebrated Keller-Segel system, with the main novelty be…
Slow growth of solutions of super-fast diffusion equations with unbounded initial data
Marek Fila, Michael Winkler
We study positive solutions of the super-fast diffusion equation in the whole space with initial data which are unbounded as . We find an explicit dependence of the s…
Global weak solutions to a strongly degenerate haptotaxis model
Michael Winkler, Christina Surulescu
We consider a one-dimensional version of a model obtained in [C. Engwer, A. Hunt, and C. Surulescu: Effective equations for anisotropic glioma spread with proliferation: a multisca…