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Publications Influence

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

A Combined Chemotaxis-haptotaxis System: The Role of Logistic Source

TLDR

62 9

Locally bounded global solutions in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion

- Y. Tao, M. Winkler
- Mathematics
- 2013

Abstract This paper deals with a boundary-value problem in three-dimensional smoothly bounded domains for a coupled chemotaxis-Stokes system generalizing the prototype { n t + u ⋅ ∇ n = Δ n m − ∇ ⋅ (… Expand

131 9- PDF

Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis–fluid system

- Y. Tao, M. Winkler
- Mathematics
- 3 June 2015

AbstractThe coupled chemotaxis–fluid system
$$\left\{ \begin{array}{lll} &n_t + u\cdot \nabla n = \Delta n - \nabla \cdot (n \nabla c) +rn-\mu n^2, \\ & c_t + u\cdot \nabla c = \Delta c-c+n , \\ &… Expand

112 8- PDF

A Chemotaxis-Haptotaxis Model: The Roles of Nonlinear Diffusion and Logistic Source

- Y. Tao, M. Winkler
- Mathematics, Computer Science
- SIAM J. Math. Anal.
- 9 March 2011

TLDR

143 7

Effects of signal-dependent motilities in a Keller–Segel-type reaction–diffusion system

- Y. Tao, M. Winkler
- Mathematics
- 23 May 2017

This work considers the Keller–Segel-type parabolic system ut = Δ(uϕ(v)), x ∈ Ω,t > 0, vt = Δv − v + u,x ∈ Ω,t > 0, (⋆) in a smoothly bounded convex domain Ω ⊂ ℝn, n ≥ 2, under no-flux boundary… Expand

33 7- PDF

Global solution for a chemotactic-haptotactic model of cancer invasion

This paper deals with a mathematical model of cancer invasion of tissue recently proposed by Chaplain and Lolas. The model consists of a reaction–diffusion-taxis partial differential equation (PDE)… Expand

78 6

Energy-type estimates and global solvability in a two-dimensional chemotaxis–haptotaxis model with remodeling of non-diffusible attractant

- Y. Tao, M. Winkler
- Mathematics
- 1 August 2014

This paper deals with the coupled chemotaxis–haptotaxis model
{ut=Δu−χ∇⋅(u∇v)−ξ∇⋅(u∇w)+μu(1−u−w),x∈Ω,t>0,0=Δv+u−v,x∈Ω,t>0,wt=−vw+ηw(1−w−u),x∈Ω,t>0,
which was initially proposed by Chaplain and… Expand

88 6

Eventual smoothness and stabilization of large-data solutions in a three-dimensional chemotaxis system with consumption of chemoattractant

- Y. Tao, M. Winkler
- Mathematics
- 1 February 2012

Abstract This paper deals with positive solutions of { u t = Δ u − ∇ ⋅ ( u ∇ v ) , x ∈ Ω , t > 0 , v t = Δ v − u v , x ∈ Ω , t > 0 , under homogeneous Neumann boundary conditions in bounded convex… Expand

154 6

Global existence of classical solutions to a combined chemotaxis–haptotaxis model with logistic source

- Y. Tao
- Mathematics
- 1 June 2009

Abstract This paper deals with a mathematical model of cancer invasion of tissue. The model consists of a system of reaction–diffusion-taxis partial differential equations describing interactions… Expand

67 6- PDF

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