Boundedness and stabilization in a two‐species chemotaxis‐competition system of parabolic‐parabolic–elliptic type
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DOI: 10.1002/mma.4607
Abstract: This paper is concerned with the two-species chemotaxis-competition system ut=d1Δu−χ1∇·(u∇w)+μ1u(1−u−a1v)inΩ×(0,∞),vt=d2Δv−χ2∇·(v∇w)+μ2v(1−a2u−v)inΩ×(0,∞),0=d3Δw+αu+βv−γwinΩ×(0,∞), where Ω is a bounded domain in Rn with smooth boundary ∂Ω, n≥2; χi and μi are constants satisfying some conditions. The above system was… read more here.
Keywords: competition system; system; species chemotaxis; chemotaxis competition ... See more keywords
Global weak solutions and eventual smoothness in a 3D two‐competing‐species chemotaxis‐Navier‐Stokes system with two consumed signals
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DOI: 10.1002/mma.6154
Abstract: This paper deals with a two‐competition‐species chemotaxis‐Navier‐Stokes system with two different consumed signals (n1)t+u·∇n1=d1Δn1−χ1∇·(n1∇c)+μ1n1(1−n1−a1n2),inΩ×(0,∞),ct+u·∇c=d2Δc−α1cn2,inΩ×(0,∞),(n2)t+u·∇n2=d3Δn2−χ2∇·(n2∇v)+μ2n2(1−a2n1−n2),inΩ×(0,∞),vt+u·∇v=d4Δv−α2vn1,inΩ×(0,∞),ut+(u·∇)u=Δu+∇P+(β1n1+β2n2)∇ϕ,inΩ×(0,∞),∇·u=0,inΩ×(0,∞), in a smooth bounded domain Ω⊂R3 under zero Neumann boundary conditions for n1,n2,c,v , and homogeneous Dirichlet boundary condition for u… read more here.
Keywords: system; navier stokes; species chemotaxis; weak solutions ... See more keywords
Boundedness in a full parabolic two-species chemotaxis system
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DOI: 10.1016/j.crma.2016.10.024
Abstract: Abstract This paper is concerned with the two-species chemotaxis system { u t = △ u − ∇ ⋅ ( u χ 1 ( w ) ∇ w ) + μ 1 u ( 1… read more here.
Keywords: boundedness full; system; chemotaxis system; species chemotaxis ... See more keywords
Boundedness in a two-species chemotaxis-consumption system with nonlinear diffusion and sensitivity
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DOI: 10.1080/00036811.2020.1721478
Abstract: This paper deals with the following two-species chemotaxis system ut=∇⋅(D1(u)∇u)−∇⋅(S1(u)∇w)+μ1u(1−u−a1v),x∈Ω, t>0,vt=∇⋅(D2(v)∇v)−∇⋅(S2(v)∇w)+μ2v(1−a2u−v),x∈Ω, t>0,wt=Δw−(u+v)w,x∈Ω, t>0 with homoge... read more here.
Keywords: boundedness two; chemotaxis consumption; consumption system; species chemotaxis ... See more keywords
Boundedness in a quasilinear two-species chemotaxis system with consumption of chemoattractant
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DOI: 10.14232/ejqtde.2019.1.31
Abstract: This paper deals with a two-species chemotaxis system ut = ∇ · (D1(u)∇u)−∇ · (uχ1(w)∇w) + μ1u(1− u− a1v), x ∈ Ω, t > 0, vt = ∇ · (D2(v)∇v)−∇ · (vχ2(w)∇w) + μ2v(1−… read more here.
Keywords: system; quasilinear two; boundedness quasilinear; chemotaxis system ... See more keywords