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The chemotaxis‐consumption system with generalized logistic source ut=Δu−∇·(uS(x,u,v)·∇v)+λu−μuα,x∈Ω,t>0,vt=Δv−uv,x∈Ω,t>0, is considered under homogeneous Neumann boundary conditions in a bounded smooth domain Ω⊂ℝn(n≥1) with suitably regular positive initial data. Here λ, μ > 0, α > 1… Click to show full abstract
The chemotaxis‐consumption system with generalized logistic source ut=Δu−∇·(uS(x,u,v)·∇v)+λu−μuα,x∈Ω,t>0,vt=Δv−uv,x∈Ω,t>0, is considered under homogeneous Neumann boundary conditions in a bounded smooth domain Ω⊂ℝn(n≥1) with suitably regular positive initial data. Here λ, μ > 0, α > 1 and S∈C2(Ω¯×[0,∞)2;ℝn×n) is a given matrix‐valued function. We construct globally defined solutions in an appropriately generalized sense and prove that these solutions converge to the spatially homogeneous equilibrium λμ1α−1,0 in the large time limit.
Journal Title: Mathematical Methods in the Applied Sciences
Year Published: 2021
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