Analysis of a chemotaxis model with indirect signal absorption

By Mario Fuest. Journal of Differential Equations, 2019

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Abstract We consider the chemotaxis model { u t = Δ u − ∇ ⋅ ( u ∇ v ) , v t = Δ v − v w , w t = − δ w + u in smooth, bounded domains Ω ⊂ R n , n ∈ N , where δ > 0 is a given parameter. If either n ≤ 2 or ‖ v 0 ‖ L ∞ ( Ω ) ≤ 1 3 n we show the existence of a unique global classical solution ( u , v , w ) and convergence of ( u ( ⋅ , t ) , v ( ⋅ , t ) , w ( ⋅ , t ) ) towards a spatially constant equilibrium, as t → ∞ . The proof of global existence for the case n ≤ 2 relies on a bootstrap procedure. As a starting point we derive a functional inequality for a functional being sublinear in u, which appears to be novel in this context.

Subfields: Modeling and Simulation, Molecular Biology, Oncology

View Paper: https://www.semanticscholar.org/paper/fe7f2f528fda3592fec8fd3b14dae0fdc91f6bf8

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Depleting the signal: Analysis of chemotaxis‐consumption models—A survey (2023, background): “15), now for p ∈ (0, 1) and a new suitable choice of φ, reveals global existence of classical solutions ([39]).”