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Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity
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 homogeneousExpand
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A Combined Chemotaxis-haptotaxis System: The Role of Logistic Source
  • Y. Tao, M. Wang
  • Computer Science, Mathematics
  • SIAM J. Math. Anal.
  • 18 September 2009
TLDR
We prove the existence, uniqueness, and uniform-in-time boundedness of global classical solutions to a chemotaxis-haptotaxis system modeling cancer invasion. Expand
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Locally bounded global solutions in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion
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
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Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis–fluid system
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
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A Chemotaxis-Haptotaxis Model: The Roles of Nonlinear Diffusion and Logistic Source
TLDR
This paper deals with a chemotaxis-haptotaxis model of cancer invasion of tissue (extracellular matrix). Expand
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Effects of signal-dependent motilities in a Keller–Segel-type reaction–diffusion system
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 boundaryExpand
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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
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Energy-type estimates and global solvability in a two-dimensional chemotaxis–haptotaxis model with remodeling of non-diffusible attractant
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 andExpand
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Eventual smoothness and stabilization of large-data solutions in a three-dimensional chemotaxis system with consumption of chemoattractant
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 convexExpand
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Global existence of classical solutions to a combined chemotaxis–haptotaxis model with logistic source
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 interactionsExpand
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