391 citations · 668 across the 36 of their papers we have counts for
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A Gagliardo-Nirenberg-type inequality and its applications to decay estimates for solutions of a degenerate parabolic equation
Marek Fila, Michael Winkler
We establish a Gagliardo-Nirenberg-type inequality in for functions which decay fast as . We use this inequality to derive upper bounds for the decay r…
Singular structure formation in a degenerate haptotaxis model involving myopic diffusion
Michael Winkler
We consider the system \[ u_t=\big(d(x)u\big)_{xx} - \big(d(x)uw_x\big)_x, \quad w_t=-ug(w), \] which arises as a simple model for haptotactic migration in heterogeneous environmen…
Global existence and stabilization in a degenerate chemotaxis-Stokes system with mildly strong diffusion enhancement
Michael Winkler
A class of chemotaxis-Stokes systems generalizing the prototype \[\left\{ \begin{array}{rcl} n_t + u\cdot\nabla n &=& \nabla \cdot \big(n^{m-1}\nabla n\big) - \nabla \cdot \big(n\n…
A generalized solution concept for the Keller-Segel system with logarithmic sensitivity: Global solvability for large nonradial data
Johannes Lankeit, Michael Winkler
The chemotaxis system \[ \left\{ \begin{array}{l} u_t = Δu - χ\nabla \cdot (\frac{u}{v}\nabla v), v_t=Δv - v+u, \end{array} \right. \] is considered in a bounded domain $Ω\subset \…