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Publications Influence

Global Large-Data Solutions in a Chemotaxis-(Navier–)Stokes System Modeling Cellular Swimming in Fluid Drops

- M. Winkler
- Mathematics
- 23 January 2012

In the modeling of collective effects arising in bacterial suspensions in fluid drops, coupled chemotaxis-(Navier–)Stokes systems generalizing the prototype have been proposed to describe the… Expand

251 27- PDF

Boundedness in the Higher-Dimensional Parabolic-Parabolic Chemotaxis System with Logistic Source

- M. Winkler
- Mathematics
- 7 July 2010

We consider nonnegative solutions of the Neumann boundary value problem for the chemotaxis system in a smooth bounded convex domain Ω ⊂ ℝ n , n ≥ 1, where τ > 0, χ ∈ ℝ and f is a smooth function… Expand

358 21

A Chemotaxis System with Logistic Source

- J. I. Tello, M. Winkler
- Mathematics
- 6 June 2007

This paper deals with a nonlinear system of two partial differential equations arising in chemotaxis, involving a source term of logistic type. The existence of global bounded classical solutions is… Expand

308 21- PDF

Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity

- Y. Tao, M. Winkler
- Physics, Mathematics
- 27 June 2011

Abstract We consider the quasilinear parabolic–parabolic Keller–Segel system { u t = ∇ ⋅ ( D ( u ) ∇ u ) − ∇ ⋅ ( S ( u ) ∇ v ) , x ∈ Ω , t > 0 , v t = Δ v − v + u , x ∈ Ω , t > 0 , under homogeneous… Expand

362 21- PDF

Boundedness vs. blow-up in a chemotaxis system

- D. Horstmann, M. Winkler
- Mathematics
- 1 August 2005

Abstract We determine the critical blow-up exponent for a Keller–Segel-type chemotaxis model, where the chemotactic sensitivity equals some nonlinear function of the particle density. Assuming some… Expand

514 16- PDF

Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system

- M. Winkler
- Mathematics
- 18 December 2011

We study the Neumann initial-boundary value problem for the fully parabolic Keller-Segel system u_t=\Delta u - \nabla \cdot (u\nabla v), \qquad x\in\Omega, \ t>0, [1mm] v_t=\Delta v-v+u, \qquad… Expand

451 15- PDF

Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues

- N. Bellomo, N. Bellomo, A. Bellouquid, Youshan Tao, M. Winkler
- Mathematics
- 28 May 2015

This paper proposes a survey and critical analysis focused on a variety of chemotaxis models in biology, namely the classical Keller–Segel model and its subsequent modifications, which, in several… Expand

442 14

Global weak solutions in a three-dimensional chemotaxis–Navier–Stokes system

- M. Winkler
- Mathematics
- 1 September 2016

Abstract The chemotaxis–Navier–Stokes system (0.1) { n t + u ⋅ ∇ n = Δ n − ∇ ⋅ ( n χ ( c ) ∇ c ) , c t + u ⋅ ∇ c = Δ c − n f ( c ) , u t + ( u ⋅ ∇ ) u = Δ u + ∇ P + n ∇ Φ , ∇ ⋅ u = 0 , ( ⋆ ) is… Expand

135 14- PDF

Global solutions in a fully parabolic chemotaxis system with singular sensitivity

- M. Winkler
- Mathematics
- 30 January 2011

The Neumann boundary value problem for the chemotaxis system
is considered in a smooth bounded domain Ω⊂ℝn, n⩾2, with initial data and v0∈W1, ∞(Ω) satisfying u0⩾0 and v0>0 in . It is… Expand

122 12- PDF

Stabilization in a two-species chemotaxis system with a logistic source

- J. I. Tello, M. Winkler
- Mathematics, Geography
- 1 May 2012

We study a system of three partial differential equations modelling the spatio-temporal behaviour of two competitive populations of biological species both of which are attracted chemotactically by… Expand

89 11- PDF

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