2024/01/31 by Shohei Kohatsu, Kohatsu, Shohei, Johannes Lankeit +1
Mathematics · #Mathematical Biology Tumor Growth
paper · pdf · doi:10.48550/arxiv.2401.17521
This paper deals with the two-species chemotaxis system with Lotka-Volterra competitive kinetics, \begincases ut = d1 Δu - χ1 ∇ ⋅ (u ∇ w) + μ1 u (1 - u - a1 v), amp; x∈Ω, tgt;0,
vt = d2 Δv - χ2 ∇ ⋅ (v ∇ w) + μ2 v (1 - a2 u - v), amp; x∈Ω, tgt;0,
0 = d3 Δw + αu + βv - γw, amp; x∈Ω, tgt;0, \endcases under homogeneous Neumann boundary conditions and suitable initial conditions, where Ω⊂ ℝn (n ∈ ℕ) is a bounded domain with smooth boundary, d1, d2, d3, χ1, χ2, μ1, μ2 > 0, a1, a2 ≥ 0 and α, β, γ> 0. Under largeness conditions on χ1 and χ2, we show that for suitably regular initial data, any thresholds of the population density can be surpassed, which extends the previous results to the non-symmetric case. The paper contains a well-posedness result for the hyperbolic-elliptic limit system with d1=d2=0.