2020/05/20 by Zhen, Chen
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2005.09915
This paper deals with the oncolytic virotherapy model \beginsplit \begincases amp;ut = Δu - ∇ ⋅ (u∇ v)-uz +μu(1-u),amp;
amp;vt = - (u+w)v,amp;
amp;wt = Dw Δw - w + uz,amp;
amp;zt = Dz Δz - z - uz + βw,amp; \endcases \endsplit in a bounded domain Ω ⊂ ℝ2 with smooth boundary, where μ, Dw, Dz and β are prescribed positive parameters. For any given suitably regular initial data, the global existence of classical solution to the corresponding homogeneous Neumann initial-boundary problem for a more general model allowing μ=0 was previously verified in [Y. Tao & M. Winkler, J. Differential Equations 268 (2020), 4973-4997]. This work further shows that whenever μ>0, the above-mentioned global classical solution to the above equation is uniformly bounded; and moreover, if β<1, then the solution (u, v, w, z) stabilizes to the constant equilibrium (1, 0, 0, 0) in the topology Lp(Ω)× (L^∞(Ω))3 with any p>1 in a large time limit.