论文标题
在溶瘤病毒疗法的HAPTOTXIS模型中，空间同质性的渐近稳定性
Asymptotic stability of spatial homogeneity in a haptotxis model for oncolytic virotherapy
论文作者
论文摘要
这项工作考虑了溶瘤病毒疗法的模型，如反应 - 扩散税系统$$ \ left \ left \ {\ oken {array} {l} {l} u_t =Δu-\ nabla \ cdot（u \ nabla v）-ppect（u \ nabla V） -w + uz，\\ [1mm] z_t =d_zΔz -z -z -uz +βW，\ end {array} \ right。 $$在平稳界限的域中$ω\ subset \ mathbb {r}^2 $，带有参数$ d_w> 0，d_z> 0，d_z> 0，β> 0 $和$ρ\ ge 0 $。每当$β> 1 $和$ \ frac {1} {|ω|} \int_ΩU（\ cdot，0）> \ frac {1} {1} {β-1} $，无限时间爆破至少在$ρ= 0 $ρ= 0 $。\ abs％。 为了提供适当的补充，目前的工作表明，对于任何$ρ\ ge 0 $和任意$β> 0 $ （γ，0,0,0）$中所有初始数据都导致全球限制的解决方案，这些解决方案稳定在恒定平衡$（u_ \ infty，0,0,0）$的情况下，其中一些$ u_ \ infty> 0 $。
This work considers a model for oncolytic virotherapy, as given by the reaction-diffusion-taxis system $$ \left\{ \begin{array}{l} u_t = Δu - \nabla \cdot (u\nabla v)-ρuz, \\[1mm] v_t = - (u+w)v, \\[1mm] w_t = D_w Δw - w + uz, \\[1mm] z_t = D_z Δz - z - uz + βw, \end{array} \right. $$ in a smoothly bounded domain $Ω\subset\mathbb{R}^2$, with parameters $D_w>0, D_z>0, β>0$ and $ρ\ge 0$.\\ % 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 $\frac{1}{|Ω|}\int_Ω u(\cdot,0)>\frac{1}{β-1}$, 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 $ρ\ge 0$ and arbitrary $β>0$, at each prescribed level $γ\in (0,\frac{1}{(β-1)_+})$ one can identify an $L^\infty$-neighborhood of the homogeneous distribution $(u,v,w,z)\equiv (γ,0,0,0)$ within which all initial data lead to globally bounded solutions that stabilize toward the constant equilibrium $(u_\infty,0,0,0)$ with some $u_\infty>0$.
