论文标题
在抛物线趋化趋化模型中的长期行为
Long-term behaviour in a parabolic-elliptic chemotaxis-consumption model
论文作者
论文摘要
趋化性系统的经典解决方案的全球存在和界限 n_t＆=Δn-\ nabla \ cdot（n \ nabla c），\\ 0＆=ΔC-nc，\ end {align*}在$ n $的无升华边界条件下，robin型边界条件\ [ \partial_νc =（γ-c）g \ \]对于$ c $（使用$γ> 0 $和$ c^{1+β}（\partialΩ）\ ni g> 0 $，对于某些$β\ in（0,1）$，在有界域$β\ subset $ω\ subset \ subset \ subset \ subset \ subset \ subset \ mathbb {$ n}中建立。此外，在$γ$的较小条件下，我们显示了与固定溶液的收敛。
Global existence and boundedness of classical solutions of the chemotaxis--consumption system \begin{align*} n_t &= Δn - \nabla \cdot (n \nabla c), \\ 0 &= Δc - nc, \end{align*} under no-flux boundary conditions for $n$ and Robin-type boundary conditions \[ \partial_ν c = (γ-c) g \] for $c$ (with $γ>0$ and $C^{1+β}(\partialΩ) \ni g > 0$ for some $β\in(0,1)$) are established in bounded domains $Ω\subset\mathbb{R}^{N}$, $N\ge 1$. Under a smallness condition on $γ$, moreover, we show convergence to the stationary solution.
