Boundedness criteria for a chemotaxis consumption model with gradient nonlinearities

2024/08/26 by Columbu, Alessandro · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.14250

Abstract

This work deals with the consumption chemotaxis problem \begincases* u_t = Δu - χ∇ ⋅ u∇ v + λu - μu² - c | ∇ u |^γ, amp; in Ω×(0,\tmax), v_t = Δv - uv, amp; in Ω×(0,\tmax), \endcases* in a bounded and smooth domain Ω⊂\Rⁿ, n≥ 3, under Neumann boundary conditions, for χ,λ,μ,c>0, \tmax∈(0,∞] and for u₀,v₀ positive initial data with a certain regularity. We will show that the problem has a unique and uniformly bounded classical solution for γ∈((2n)/(n+1),2]. Moreover, we have the same result for γ=(2n)/(n+1) and a condition that involves the parameters c,μ,n,χ and the initial data.

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• Global dynamics of chemotaxis-consumption systems with oppositely acting nonlocal terms

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