论文标题
在准抛物线抛物线 - 纤维化 - 纤维化吸引力 - 抑制趋化系统中，稳定质量的稳定性依赖于密度的灵敏度：抑制为主导的情况
Stabilization for small mass in a quasilinear parabolic--elliptic--elliptic attraction-repulsion chemotaxis system with density-dependent sensitivity: repulsion-dominant case
论文作者
论文摘要
本文涉及quasilinear吸引力 - 抑制趋化性系统\ begin {align*} \ begin {case} u_t = \ nabla \ cdot \ big（（U+1）^{m-1} \ nabla u -χu（u+1）^{p-2} \ nabla v +ξu（u+1）^{q-2} \ nabla w \ big），\\ [] 0 =ΔV+αu-βv，\\ [] 0 =ΔW+γu-ΔW \ end {cases} \ end {align*}在有界域$ω\ subset \ mathbb {r}^n $ $（n \ in \ mathbb {n}）$带有光滑边界$ \ partialω$的$ m，p，q \ in \ mathbb in \ mathbb in \ mathbb {r} $，常数。在$ m = 1 $和$ p = q = 2 $的情况下，当$χα-ξγ<0 $和$β=δ$，tao-wang（数学模型方法应用程序； 2013; 2013; 23; 1-36; 1-36; 1-36）证明了全球有限的经典跨越空间上的常数平衡$（通过使用转换$ z：=χV-ξw$，\fracγδ\叠加{u_0}）$通过keller-segel系统的减少，其中$ \ overline {u_0} $是初始数据$ u_0 $的空间平均值。但是，由于上述系统涉及非线性，因此该方法不再有效。本文的目的是确定全局有限的经典解决方案会收敛到空间恒定的平衡$（\ overline {u_0}，\fracαβ\ overline {u_0}，\fracγδ\ overline {u_0}）$。
This paper deals with the quasilinear attraction-repulsion chemotaxis system \begin{align*} \begin{cases} u_t=\nabla\cdot \big((u+1)^{m-1}\nabla u -χu(u+1)^{p-2}\nabla v +ξu(u+1)^{q-2}\nabla w\big),\\[] 0=Δv+αu-βv,\\[] 0=Δw+γu-δw \end{cases} \end{align*} in a bounded domain $Ω\subset \mathbb{R}^n$ $(n \in \mathbb{N})$ with smooth boundary $\partial Ω$, where $m, p, q \in \mathbb{R}$, $χ, ξ, α, β, γ, δ>0$ are constants. In the case that $m=1$ and $p=q=2$, when $χα-ξγ<0$ and $β=δ$, Tao-Wang (Math. Models Methods Appl. Sci.; 2013; 23; 1-36) proved that global bounded classical solutions toward the spatially constant equilibrium $(\overline{u_0}, \fracαβ\overline{u_0}, \fracγδ\overline{u_0})$ via the reduction to the Keller-Segel system by using the transformation $z:=χv-ξw$, where $\overline{u_0}$ is the spatial average of the initial data $u_0$. However, since the above system involves nonlinearities, the method is no longer valid. The purpose of this paper is to establish that global bounded classical solutions converge to the spatially constant equilibrium $(\overline{u_0}, \fracαβ\overline{u_0}, \fracγδ\overline{u_0})$.
