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Publications Influence

Eventual smoothness and asymptotics in a three-dimensional chemotaxis system with logistic source

- Johannes Lankeit
- Physics, Mathematics
- 18 July 2014

Abstract We prove existence of global weak solutions to the chemotaxis system u t = Δ u − ∇ ⋅ ( u ∇ v ) + κ u − μ u 2 v t = Δ v − v + u under homogeneous Neumann boundary conditions in a smooth… Expand

124 5- PDF

Long-term behaviour in a chemotaxis-fluid system with logistic source

- Johannes Lankeit
- Physics, Mathematics
- 1 February 2016

We consider the coupled chemotaxis Navier–Stokes model with logistic source terms: nt + u ⋅∇n = Δn − χ∇⋅ (n∇c) + κn − μn2, ct + u ⋅∇c = Δc − nc, ut + (u ⋅∇)u = Δu + ∇P + n∇Φ + f,∇⋅ u = 0 in a… Expand

83 4- PDF

The Exponentiated Hencky-Logarithmic Strain Energy. Part I: Constitutive Issues and Rank-One Convexity

- P. Neff, I. Ghiba, Johannes Lankeit
- Mathematics, Physics
- 15 March 2014

We investigate a family of isotropic volumetric-isochoric decoupled strain energies $$\begin{aligned} F\mapsto W_{\mathrm{eH}}(F):=\widehat{W}_{\mathrm{eH}}(U):=\left \{ \begin{array}{l@{\quad}l}… Expand

62 3- PDF

Chemotaxis can prevent thresholds on population density

- Johannes Lankeit
- Mathematics
- 7 March 2014

We define and (for $q>n$) prove uniqueness and an extensibility property of $W^{1,q}$-solutions to
$u_t =-\nabla\cdot(u\nabla v)+\kappa u-\mu u^2$
$ 0 =\Delta v-v+u$
$\partial_\nu… Expand

78 3- PDF

Locally bounded global solutions to a chemotaxis consumption model with singular sensitivity and nonlinear diffusion

- Johannes Lankeit
- Mathematics
- 18 August 2016

We show the existence of locally bounded global solutions to the chemotaxis system \[ u_t = \nabla\cdot(D(u)\nabla u) - \nabla\cdot(\frac{u}{v} \nabla v) \] \[ v_t = \Delta v - uv \] with homogeneous… Expand

42 3- PDF

Global classical small-data solutions for a three-dimensional chemotaxis Navier–Stokes system involving matrix-valued sensitivities

- Xinru Cao, Johannes Lankeit
- Physics, Mathematics
- 15 January 2016

The coupled chemotaxis fluid system $$\begin{aligned} \left\{ \begin{array}{lll} n_t=\Delta n-\nabla \cdot (n S(x,n,c)\cdot \nabla c)-u\cdot \nabla n, &{}\quad (x,t)\in \Omega \times (0,T),\\… Expand

78 3- PDF

Global existence, boundedness and stabilization in a high-dimensional chemotaxis system with consumption

- Johannes Lankeit, Yulan Wang
- Mathematics
- 29 August 2016

This paper deals with the homogeneous Neumann boundary-value problem for the chemotaxis-consumption system \begin{eqnarray*} \begin{array}{llc} u_t=\Delta u-\chi\nabla\cdot (u\nabla v)+\kappa u-\mu… Expand

40 3- PDF

A new approach toward boundedness in a two-dimensional parabolic chemotaxis system with singular sensitivity

- Johannes Lankeit
- Mathematics
- 21 January 2015

We consider the parabolic chemotaxis model \[ u_t=\Delta u - \chi \nabla\cdot(\frac uv \nabla v), \qquad\qquad v_t=\Delta v - v + u\] in a smooth, bounded, convex two-dimensional domain and show… Expand

59 3- PDF

A generalized solution concept for the Keller–Segel system with logarithmic sensitivity: global solvability for large nonradial data

- Johannes Lankeit, M. Winkler
- Physics, Mathematics
- 25 January 2017

The chemotaxis system $$\begin{aligned} \left\{ \begin{array}{l} u_t = \Delta u - \chi \nabla \cdot \left( \frac{u}{v}\nabla v\right) , \\ v_t=\Delta v - v+u, \end{array} \right.… Expand

58 2- PDF

On the weakly competitive case in a two-species chemotaxis model

- T. Black, Johannes Lankeit, Masaaki Mizukami
- Mathematics
- 12 April 2016

In this article we investigate a parabolic-parabolic-elliptic two-species chemotaxis system with weak competition and show global asymptotic stability of the coexistence steady state under a… Expand

44 1- PDF

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