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Global Large-Data Solutions in a Chemotaxis-(Navier–)Stokes System Modeling Cellular Swimming in Fluid Drops
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 theExpand
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Boundedness in the Higher-Dimensional Parabolic-Parabolic Chemotaxis System with Logistic Source
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 functionExpand
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A Chemotaxis System with Logistic Source
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 isExpand
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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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Boundedness vs. blow-up in a chemotaxis system
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 someExpand
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Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system
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, \qquadExpand
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Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues
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 severalExpand
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Global weak solutions in a three-dimensional chemotaxis–Navier–Stokes system
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 , ( ⋆ ) isExpand
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Global solutions in a fully parabolic chemotaxis system with singular sensitivity
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 isExpand
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Stabilization in a two-species chemotaxis system with a logistic source
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 byExpand
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