2020/06/09 by Youshan Tao, Michael Winkler, Tao, Youshan +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #35B33 #35B40 #35K57 #35Q92 #92C17 #Analysis of PDEs (math.AP) #Evolution and Genetic Dynamics #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models
paper · pdf · doi:10.48550/arxiv.2006.05293
openalex publication_date 2020/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work considers a model for oncolytic virotherapy, as given by the reaction-diffusion-taxis system \ ut = Δu - ∇ ⋅ (u∇ v)-ρuz,
vt = - (u+w)v,
wt = Dw Δw - w + uz,
zt = Dz Δz - z - uz + βw, . in a smoothly bounded domain Ω⊂ℝ2, with parameters Dw>0, Dz>0, β>0 and ρ≥ 0. % Previous analysis has asserted that for all reasonably regular initial data, an associated no-flux type initial-boundary value problem admits a global classical solution, and that this solution is bounded if β<1, whereas whenever β>1 and (1)/(|Ω|)∫Ω u(⋅,0)>(1)/(β-1), infinite-time blow-up occurs at least in the particular case when ρ=0.\abs % In order to provide an appropriate complement to this, the present work reveals that for any ρ≥ 0 and arbitrary β>0, at each prescribed level γ∈ (0,(1)/((β-1)+)) one can identify an L^∞-neighborhood of the homogeneous distribution (u,v,w,z)≡ (γ,0,0,0) within which all initial data lead to globally bounded solutions that stabilize toward the constant equilibrium (u_∞,0,0,0) with some u_∞>0.