4 citations · 10 across the 5 of their papers we have counts for
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Stability vs. instability of singular steady states in the parabolic-elliptic Keller-Segel system on
Francesca Colasuonno, Michael Winkler
The Cauchy problem in is considered for \begin{eqnarray*} \left\{ \begin{array}{l} u_t = Δu - \nabla \cdot (u\nabla v),\\ 0 = Δv + u. \end{array} \right. \end{eqnarra…
Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities
Genglin Li, Michael Winkler
We consider the Keller-Segel-type migration-consumption system involving signal-dependent motilities, $$\left\{ \begin{array}{l} u_t = Δ\big(uϕ(v)\big), \\[1mm] v_t = Δv-uv, \end{a…
Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities
Genglin Li, Michael Winkler
Two relaxation features of the migration-consumption chemotaxis system involving signal-dependent motilities, $$ \left\{ \begin{array}{l} u_t = Δ\big(uϕ(v)\big), \\[1mm] v_t = Δv-u…
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…