9 citations · 26 across the 16 of their papers we have counts for
25 papers
Phenotype switching in chemotaxis aggregation models controls the spontaneous emergence of large densities
Kevin J Painter, Michael Winkler
We consider a phenotype-switching chemotaxis model for aggregation, in which a chemotactic population is capable of switching back and forth between a chemotaxing state (performing…
A quantitative strong parabolic maximum principle and application to a taxis-type migration-consumption model involving signal-dependent degenerate diffusion
Michael Winkler
The taxis-type migration-consumption model accounting for signal-dependent motilities, as given by \[ u_t = Δ\big(uϕ(v)\big), v_t = Δv-uv, \qquad (*) \] is considered for suitably…
Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing
Laurent Desvillettes, Philippe Laurençot, Ariane Trescases +1
New estimates and global existence results are provided for a class of systems of cross diffusion equations arising from the modeling of chemotaxis with local sensing, possibly fea…
Global existence in reaction-diffusion systems with mass control under relaxed assumptions merely referring to cross-absorptive effects
Johannes Lankeit, Michael Winkler
We introduce a generalized concept of solutions for reaction-diffusion systems and prove their global existence. The only restriction on the reaction function beyond regularity, qu…
A double critical mass phenomenon in a no-flux-Dirichlet Keller-Segel system
Jan Fuhrmann, Johannes Lankeit, Michael Winkler
Derived from a biophysical model for the motion of a crawling cell, the system \[(*)~\begin{cases}u_t=Δu-\nabla\cdot(u\nabla v)\\0=Δv-kv+u\end{cases}\] is investigated in a finite…
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…