Asymptotic homogenization in a three-dimensional nutrient taxis system involving food-supported proliferation

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Depleting the signal: Analysis of chemotaxis‐consumption models—A survey (2023, background): “…in Theorem 16 we have where (𝑢 ⋆ , 𝑣 ⋆ ) ∈ (0, ∞) × (0, 𝑠 0 ) is the unique solution of the algebraic system Precedents and close relatives concerned with questions of global solvability, boundedness and spatially homogeneous asymptotics in (CC7), and neighboring systems can be found in Refs.”
A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion (2022, background): “[32], [19], [39] for some small selection of examples).”
Large time behavior in a predator-prey system with indirect pursuit-evasion interaction (2017, background): “4) in which analytical findings indicate that at least in two-dimensional settings, the additional dissipation generated by the absorptive term −uv therein may rule out the occurrence of blow-up under various assumptions on χ or on local kinetics functions f and g0 ([19], [27]; cf.”