• Publications
  • Influence
Eventual smoothness and asymptotics in a three-dimensional chemotaxis system with logistic source
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 smoothExpand
  • 124
  • 5
  • PDF
Long-term behaviour in a chemotaxis-fluid system with logistic source
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 aExpand
  • 83
  • 4
  • PDF
The Exponentiated Hencky-Logarithmic Strain Energy. Part I: Constitutive Issues and Rank-One Convexity
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
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_\nuExpand
  • 78
  • 3
  • PDF
Locally bounded global solutions to a chemotaxis consumption model with singular sensitivity and nonlinear diffusion
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 homogeneousExpand
  • 42
  • 3
  • PDF
Global classical small-data solutions for a three-dimensional chemotaxis Navier–Stokes system involving matrix-valued sensitivities
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
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-\muExpand
  • 40
  • 3
  • PDF
A new approach toward boundedness in a two-dimensional parabolic chemotaxis system with singular sensitivity
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 showExpand
  • 59
  • 3
  • PDF
A generalized solution concept for the Keller–Segel system with logarithmic sensitivity: global solvability for large nonradial data
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
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 aExpand
  • 44
  • 1
  • PDF
...
1
2
3
4
5
...