Stationary states of a chemotaxis consumption system with singular sensitivity and inhomogeneous boundary conditions

2024/06/26 by Ahn, Jaewook, Lankeit, Johannes
#35J25 #35Q92 #92C17 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.18750

Abstract

For given total mass m>0 we show unique solvability of the stationary chemotaxis-consumption model \begincases 0= Δu - χ∇ ⋅ ((u)/(v) ∇ v)
0= Δv - uv
∫_Ωu = m \endcases under no-flux-Dirichlet boundary conditions in bounded smooth domains Ω⊂ ℝ² and Ω=B_R(0)⊂ ℝ^d, d≥ 3.

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